Biomechanical Basis of Human Movement, 3rd Edition
Appendices
Appendix A: The Metric System and SI Units
All measurements in the biomechanics literature are expressed in terms of the metric system. This system of measurement uses units that are related to one another by some power of 10. Table A-1 presents the prefixes associated with these powers.
The standard length in the metric system is the meter. This standard measure was originally indicated by two scratches on a platinum-iridium alloy bar kept at the International Bureau of Weights and Measures in Sèvres, France. Table A-2 illustrates the use of these prefixes in common units of length.
The uniform system for the reporting of numerical values is known as the Système International d'Unites, or SI. This system was developed through international cooperation to standardize the report of scientific information. The base dimensions used in biomechanics are mass, length, time, temperature, electric current, amount of substance, and luminous intensity. The base units in SI corresponding to the base dimensions are the kilogram, the meter, the second, and the degree kelvin. Table A-3 presents the base units of SI.
Other units of measurement that are used in biomechanics are derived. These units are presented in Table A-4. Common conversions are shown in Table A-5.
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TABLE A-1 Prefixes for the Powers of 10
|
|
Prefix
|
Multiplier
|
Symbol
|
Example
|
|
Giga
|
109
|
G
|
Gigabyte (Gb)
|
|
Mega
|
106
|
M
|
Megawatt (MW)
|
|
Kilo
|
103
|
k
|
Kilogram (kg)
|
|
Centi
|
10–2
|
c
|
Centimeter (cm)
|
|
Milli
|
10–3
|
m
|
Milligram (mg)
|
|
Micro
|
10–6
|
µ
|
Microsecond (µs)
|
|
Nano
|
10–9
|
v
|
Nanosecond (ns)
|
|
|
TABLE A-2 Units of Length
|
|
Metric Unit
|
Power
|
Symbol
|
|
Kilometer
|
10–3
|
km
|
|
Meter
|
–
|
m
|
|
Decimeter
|
10–1
|
dm
|
|
Centimeter
|
10–2
|
cm
|
|
Millimeter
|
10–3
|
mm
|
|
Micrometer
|
10–6
|
µm
|
|
|
TABLE A-3 Base Units of Measurement
|
|
Dimension
|
Unit
|
Symbol
|
|
Mass
|
Kilogram
|
kg
|
|
Length
|
Meter
|
m
|
|
Time
|
Second
|
s
|
|
Temperature
|
Degree kelvin
|
K
|
|
Electrical current
|
Ampere
|
A
|
|
Amount of substance
|
Mole
|
Mol
|
|
Luminous intensity
|
Candela
|
cd
|
|
|
TABLE A-4 Derived units of measurement
|
|
Dimension
|
Unit
|
Symbol
|
|
Acceleration
|
Meters per second squared
|
m/s2
|
|
Angle
|
Radian
|
rad
|
|
Area
|
Meter squared
|
m2
|
|
Capacitance
|
Farad
|
F
|
|
Concentration
|
Moles per meter cubed
|
mol/m3
|
|
Density
|
Mass per unit volume
|
kg/m3
|
|
Energy
|
Joule
|
J
|
|
Impulse
|
Force × time
|
N5
|
|
Luminous flux
|
Lumen
|
lm
|
|
Moment of inertia
|
Kilogram-meters squared
|
kgm2
|
|
Momentum
|
Kilogram-meters per second
|
kgm/s
|
|
Power
|
Watts
|
W
|
|
Pressure
|
Pascal
|
Pa
|
|
Resistance
|
Ohm
|
Ω
|
|
Speed
|
Meters per second
|
m/s
|
|
Torque
|
Newton meter
|
Nm
|
|
Voltage
|
Volt
|
V
|
|
Volume
|
Meter cubed
|
m3
|
|
Work
|
Joule
|
J
|
|
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|
TABLE A-5 Common Conversions
|
|
Length
|
|
1 inch = 25.40 mm
|
1 inch = 2.54 cm
|
1 foot = 0.3048 m
|
1 foot= 30.48 cm
|
|
1 yard = 0.9144 m
|
1 mile = 1609.34 m
|
1 cm = 0.3937 inches
|
1 cm = 0.0328 feet
|
|
1 m = 39.37 inches
|
1 m = 3.2808 feet
|
1 m = 1.0936 yard
|
1 m = .0936 yard
|
|
1 km =0.6214 miles
|
|
Area
|
|
1 in =645.16 mm2
|
1 ft2 =0.0929 m2
|
1 yd2 =0.8361 m2
|
1 cm2 0.155 in2
|
|
1 m2 =10.76 ft2
|
|
Volume
|
|
1 in3 =16.387 cm3
|
1 ft3 =.0283 m3
|
1 yd3 =0.7645 m3
|
1 yd3 0.7645 m3
|
|
1 cm3 =0.061 in3
|
1 m3 =35.32 ft3
|
1 m3 =1.308 yd3
|
|
|
Mass
|
|
1 oz = 28.349 g
|
1 lb = 0.4536 kg
|
1 slug = 14.5939 kg
|
1 slug = 32.2 lb
|
|
1 g = 0.0353 oz.
|
1 kg = 2.2046 lb
|
1 kg = 0.0685 slug
|
|
|
Density
|
|
1 lb-ft3 = 16.02 kg/m3
|
1 slug-ft3 = 515.38 kg/m3
|
|
|
Moment of Inertia
|
|
1 slug-ft2 = 1.36 kgm2
|
1 lb-ft2 = 0.042 kgm2
|
|
|
Velocity
|
|
1 in/s = 24.4 mm/s
|
1 ft/s = 0.305 m/s
|
1 mph = 0.447 m/s
|
1 mph= 1.467 ft/s
|
|
1 m/s = 3.60 km/hr
|
1 m/s = 3.28 ft/s
|
1 m/s = 2.237 m/hr
|
1 cm/s = 0.0328 ft/s
|
|
Force
|
|
1 poundal = 0.1383 N
|
1 lb-force = 4.448 N
|
1 kg-force = 9.81 N
|
1 N = 0.102 kg
1 N = 0.2248 lb
|
|
Pressure
|
|
1 poundal/ft2 = 1.4881 Pa
1 mm mercury = 133.322 Pa
|
1 pound-force /ft2 = 47.889 Pa
|
pound-force/in2 = 6.8947 Pa
|
|
|
Work and Energy
|
|
1 foot poundal = 0.0421 J
|
1 foot pound-force = 1.3558 J
|
1 foot pound-force = 0.1383 kgm
|
1 kgm = 7.2307 ft-lb
|
|
1 BTU = 1.0551 kJ
|
1 kilocalorie = 4.1868 kJ
|
1 J = 0.7376 ft-lb
|
1 J = 0.1020 kgm
|
|
Power
|
|
1 hp (British) = 745.700 W
|
1 hp (metric) = 735.499 W
|
1 hp (metric) = 735.499 W
|
1 ft-lb force/s = 1.3558 W
|
|
Torque
|
|
1 Nm = 0.74 lb-ft
|
1 lb-ft = 1.36 Nm
|
1 kgm = 7.23 lb-ft
|
1 kg-cm = 0.0723 lb-ft
|
|
BTU, British thermal unit.
|
|
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Appendix B: Trigonometric Functions
Trigonometry is a branch of mathematics concerned with the measurements of the sides and angles of triangles and their relationships with each other. Many concepts in biomechanics require knowledge of trigonometry A triangle is composed of three sides and three angles. The sum of the three angles of a triangle equals 180°. A right triangle is a triangle in which one of the angles is a right angle, that is, one of the angles equals 90°. The sum of the remaining angles, therefore, also equals 90°. Consider the triangle with vertices A, B, and C and sides of length AB, AC, and BC in Figure B-1.
The side opposite the right angle, AB, is always the longest side in the right triangle and is referred to as the hypotenuse. The other two sides are named according to which of the other angles is under consideration. If angle A is considered, the side AC is the adjacent side, and the side BC is the opposite side. If angle B is considered (as in the triangle on the right below), BC is the adjacent side and AC is the opposite side.
Based on the right triangle, trigonometric functions may be defined. A mathematical function is a quantity whose value varies and depends on some other quantity or quantities. Trigonometric functions vary with and depend on the values of the two acute (i.e., <90°) angles in a right triangle and the lengths of the sides of the triangle. The trigonometric functions are the ratios of the lengths of the sides of the triangle based on one of the two acute angles in the triangle. There are six such functions: sine (abbreviation is sin), cosine (abbreviation is cos), tangent (abbreviation is tan), cosecant, secant, and cotangent.
In biomechanics, only the first three of these functions are important. The trigonometric functions are thus defined for angle A (Fig. B-2A) as:
- The sine of an angle is the ratio of the side opposite the angle to the hypotenuse.
- The cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse.
- The tangent of an angle is the ratio of the side opposite to the angle to the side adjacent to the angle.
Similarly, the ratios for angle B in Figure B-2B may be defined as:
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|
FIGURE B-1 A right triangle with a right angle C (90°) and two acute angles, A and B. A and B sum to 90°.
|
For any angle, the ratios formed by the sides of the right triangle will always be the same. For example, the sine of an angle of 32 will always equal 0.5299 regardless of the size of the sides of the triangle. The same is true for the cosine and tangent of the angle. The values for the sine, cosine, and tangent of angles can be presented in tables. Table B-1 presents these values for angles ranging from 0° to 90°.
| |
|
FIGURE B-2 Descriptions of the sides of a right triangle based on the acute angles A (A) and B (B).
|
|
TABLE B-1 Trigonometric Functions
|
| |
|
Angle
|
|
Degrees
|
Radian
|
Sine
|
Cosine
|
Tangent
|
| |
|
|
|
|
|
0
|
0.000
|
0.0000
|
0.0000
|
0.0000
|
|
1
|
0.017
|
0.0175
|
0.9998
|
0.0175
|
|
2
|
0.035
|
0.0349
|
0.9994
|
0.0349
|
|
3
|
0.052
|
0.0523
|
0.9986
|
0.0524
|
|
4
|
0.070
|
0.0698
|
0.9976
|
0.0699
|
|
5
|
0.087
|
0.0872
|
0.9962
|
0.0875
|
|
6
|
0.105
|
0.1045
|
0.9945
|
0.1051
|
|
7
|
0.122
|
0.1219
|
0.9925
|
0.1228
|
|
8
|
0.140
|
0.1392
|
0.9903
|
0.1405
|
|
9
|
0.157
|
0.1564
|
0.9877
|
0.1584
|
|
10
|
0.175
|
0.1736
|
0.9848
|
0.1763
|
|
11
|
0.192
|
0.1908
|
0.9816
|
0.1944
|
|
12
|
0.209
|
0.2079
|
0.9781
|
0.2126
|
|
13
|
0.227
|
0.2250
|
0.9744
|
0.2309
|
|
14
|
0.244
|
0.2419
|
0.9703
|
0.2493
|
|
15
|
0.262
|
0.2588
|
0.9659
|
0.2679
|
|
16
|
0.279
|
0.2756
|
0.9613
|
0.2867
|
|
17
|
0.297
|
0.2924
|
0.9563
|
0.3057
|
|
18
|
0.314
|
0.3090
|
0.9511
|
0.3249
|
|
19
|
0.332
|
0.3256
|
0.9455
|
0.3443
|
|
20
|
0.349
|
0.3420
|
0.9397
|
0.3640
|
|
21
|
0.367
|
0.3584
|
0.9336
|
0.3839
|
|
22
|
0.384
|
0.3746
|
0.9272
|
0.4040
|
|
23
|
0.401
|
0.3907
|
0.9205
|
0.4245
|
|
24
|
0.419
|
0.4067
|
0.9135
|
0.4452
|
|
25
|
0.436
|
0.4226
|
0.9063
|
0.4663
|
|
26
|
0.454
|
0.4384
|
0.8988
|
0.4877
|
|
27
|
0.471
|
0.4540
|
0.8910
|
0.5095
|
|
28
|
0.489
|
0.4695
|
0.8829
|
0.5317
|
|
29
|
0.506
|
0.4848
|
0.8746
|
0.5543
|
|
30
|
0.524
|
0.5000
|
0.8660
|
0.5774
|
|
31
|
0.541
|
0.5150
|
0.8572
|
0.6009
|
|
32
|
0.559
|
0.5299
|
0.8480
|
0.6249
|
|
33
|
0.576
|
0.5446
|
0.8387
|
0.6494
|
|
34
|
0.593
|
0.5592
|
0.8290
|
0.6745
|
|
35
|
0.611
|
0.5736
|
0.8192
|
0.7002
|
|
36
|
0.628
|
0.5878
|
0.8090
|
0.7265
|
|
37
|
0.646
|
0.6018
|
0.7986
|
0.7536
|
|
38
|
0.663
|
0.6157
|
0.7880
|
0.7813
|
|
39
|
0.681
|
0.6293
|
0.7771
|
0.8098
|
|
40
|
0.698
|
0.6428
|
0.7660
|
0.8391
|
|
41
|
0.716
|
0.6561
|
0.7547
|
0.8693
|
|
42
|
0.733
|
0.6691
|
0.7431
|
0.9004
|
|
43
|
0.750
|
0.6820
|
0.7314
|
0.9325
|
|
44
|
0.768
|
0.6947
|
0.7193
|
0.9657
|
|
45
|
0.785
|
0.7071
|
0.7071
|
1.0000
|
|
46
|
0.803
|
0.7193
|
0.6947
|
1.0355
|
|
47
|
0.820
|
0.7314
|
0.6820
|
1.0724
|
|
48
|
0.838
|
0.7431
|
0.6691
|
1.1106
|
|
49
|
0.855
|
0.7547
|
0.6561
|
1.1504
|
|
50
|
0.873
|
0.7660
|
0.6428
|
1.1918
|
|
51
|
0.890
|
0.7771
|
0.6293
|
1.2349
|
|
52
|
0.908
|
0.7880
|
0.6157
|
1.2799
|
|
53
|
0.925
|
0.7986
|
0.6018
|
1.3270
|
|
54
|
0.942
|
0.8090
|
0.5878
|
1.3764
|
|
55
|
0.960
|
0.8192
|
0.5736
|
1.4281
|
|
56
|
0.977
|
0.8290
|
0.5592
|
1.4826
|
|
57
|
0.995
|
0.8387
|
0.5446
|
1.5399
|
|
58
|
1.012
|
0.8480
|
0.5299
|
1.6003
|
|
59
|
1.030
|
0.8572
|
0.5150
|
1.6643
|
|
60
|
1.047
|
0.8660
|
0.5000
|
1.7321
|
|
61
|
1.065
|
0.8746
|
0.4848
|
1.8040
|
|
62
|
1.082
|
0.8829
|
0.4695
|
1.8807
|
|
63
|
1.100
|
0.8910
|
0.4540
|
1.9626
|
|
64
|
1.117
|
0.8988
|
0.4384
|
2.0503
|
|
65
|
1.134
|
0.9063
|
0.4226
|
2.1445
|
|
66
|
1.152
|
0.9135
|
0.4067
|
2.2460
|
|
67
|
1.169
|
0.9205
|
0.3907
|
2.3559
|
|
68
|
1.187
|
0.9272
|
0.3746
|
2.4751
|
|
69
|
1.204
|
0.9336
|
0.3584
|
2.6051
|
|
70
|
1.222
|
0.9397
|
0.3420
|
2.7475
|
|
71
|
1.239
|
0.9455
|
0.3256
|
2.9042
|
|
72
|
1.257
|
0.9511
|
0.3090
|
3.0777
|
|
73
|
1.274
|
0.9563
|
0.2924
|
3.2709
|
|
74
|
1.292
|
0.9613
|
0.2756
|
3.4874
|
|
75
|
1.309
|
0.9659
|
0.2588
|
3.7321
|
|
76
|
1.326
|
0.9703
|
0.2419
|
4.0108
|
|
77
|
1.344
|
0.9744
|
0.2250
|
4.3315
|
|
78
|
1.361
|
0.9781
|
0.2079
|
4.7046
|
|
79
|
1.379
|
0.9816
|
0.1908
|
5.1446
|
|
80
|
1.396
|
0.9848
|
0.1736
|
5.6713
|
|
81
|
1.414
|
0.9877
|
0.1564
|
6.3138
|
|
82
|
1.431
|
0.9903
|
0.1392
|
7.1154
|
|
83
|
1.449
|
0.9925
|
0.1219
|
8.1443
|
|
84
|
1.466
|
0.9945
|
0.1045
|
9.5144
|
|
85
|
1.484
|
0.9962
|
0.0872
|
11.4300
|
|
86
|
1.501
|
0.9976
|
0.0698
|
14.3010
|
|
87
|
1.518
|
0.9986
|
0.0523
|
19.0810
|
|
88
|
1.536
|
0.9994
|
0.0349
|
28.6360
|
|
89
|
1.553
|
0.9998
|
0.0175
|
57.2900
|
|
90
|
1.571
|
1.0000
|
0.0000
|
∞
|
|
P.469
The values in this table may also be used to determine the angle when the sides of the triangle are known. Consider the triangle in Figure B-3. The length of the hypotenuse, AC, is 0.05 m, and the length of the side opposite angle C is 0.03 m. The ratio of AB to AC is the sine of angle C. Thus:
| |
|
FIGURE B-3 A right triangle with two sides of known lengths and two unknown angles.
|
If the sine values in Table B-1 are examined, it can be determined that the angle whose sine is 0.6 is approximately 37°. This is the arcsin of the angle. Thus:
The ratio of the side AB to the hypotenuse AC is the cosine of angle A in Figure B-3. The ratio is still 0.6, and the angle whose cosine is 0.6 is approximately 53. This is referred to as the arccosine of an angle.
Two other useful trigonometric relationships are applicable to all triangles, not only right triangles. The first of these relationships is the law of sines, which states that the ratio of the length of any side to the sine of the angle opposite that side is equal to the ratio of any other side to
P.470
the angle opposite that side. Consider the triangle in Figure B-4.
| |
|
FIGURE B-4 A scalene triangle (no right angle; no two angles the same).
|
For this triangle, the law of sines can be stated as follows:
The other trigonometric relationship that is applicable to any triangle is the law of cosines. This relationship states that the square of the length of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the lengths of the other two sides and the cosine of the angle opposite the original side. Consider the triangle in Figure B-4. For side A of this triangle, the law of cosines can be stated as follows:
Similarly, the law of cosines can be stated for sides B and C.
P.471
Appendix C: Sample Kinematic and Kinetic Data
Subject: 50-kg woman
Activity: Walking sampled at 120 Hz; one cycle from right foot touchdown to right foot touchdown
Markers: Head, R shoulder, R elbow, R wrist, R hand, R crest (IC), R greater trochanter (GT), R knee, R ankle, R heel, R fifth metatarsal (met), R toe
Stride events: Right foot touchdown (RTD), left foot touchdown (LTD), right foot toe-off (RTO)
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P.476
P.477
|
TABLE C-1 Kinematic Data in Millimeters
|
|
Frame Number
|
Head x
|
Head y
|
Shoulder x
|
Shoulder Y
|
Elbow x
|
Elbow Y
|
Wrist x
|
Wrist y
|
Hand x
|
Hand y
|
IC x
|
IC Y
|
|
1
|
28.000
|
1458.867
|
155.0670
|
1340.267
|
272.4000
|
1122.533
|
337.067
|
891.2001
|
383.333
|
821.1334
|
129.6670
|
959.4000
|
|
0
|
16.1104
|
1460.070
|
142.8280
|
1340.392
|
259.5290
|
1122.318
|
323.567
|
890.5505
|
369.112
|
820.3072
|
117.0390
|
960.8488
|
|
1
|
5.8344
|
1460.187
|
132.3700
|
1339.994
|
249.0580
|
1121.832
|
313.184
|
889.9189
|
358.828
|
819.6309
|
105.7240
|
960.9595
|
|
2
|
5.5109
|
1460.400
|
120.8120
|
1339.625
|
237.4180
|
1121.333
|
301.533
|
889.244
|
347.240
|
818.8842
|
93.2708
|
961.1825
|
|
3
|
17.5563
|
1460.741
|
108.5230
|
1339.332
|
224.9500
|
1120.857
|
288.895
|
888.5603
|
334.605
|
818.0917
|
80.1029
|
961.5585
|
|
4
|
30.0691
|
1461.238
|
95.7353
|
1339.154
|
211.8550
|
1120.43
|
275.419
|
887.8932
|
321.052
|
817.2701
|
66.4896
|
962.1211
|
|
5
|
42.8924
|
1461.910
|
82.6015
|
1339.121
|
198.2620
|
1120.073
|
261.185
|
887.2629
|
306.650
|
816.4315
|
52.6116
|
962.8947
|
|
6
|
55.9139
|
1462.766
|
69.2294
|
1339.257
|
184.2630
|
1119.802
|
246.242
|
886.6854
|
291.434
|
815.5863
|
38.5936
|
963.8934
|
|
7
|
69.0503
|
1463.812
|
55.6970
|
1339.575
|
169.9210
|
1119.628
|
230.618
|
886.1729
|
275.426
|
814.7437
|
24.5215
|
965.1221
|
|
8
|
82.2388
|
1465.042
|
42.0612
|
1340.085
|
155.2870
|
1119.557
|
214.338
|
885.7347
|
258.640
|
813.9131
|
10.4521
|
966.5772
|
|
9
|
95.4311
|
1466.451
|
28.3636
|
1340.787
|
140.4000
|
1119.594
|
197.423
|
885.3776
|
241.090
|
813.1049
|
3.5790
|
968.2484
|
|
10
|
108.5901
|
1468.027
|
14.6346
|
1341.677
|
125.2930
|
1119.737
|
179.898
|
885.1063
|
222.789
|
812.3306
|
17.5514
|
970.1204
|
|
11
|
121.6875
|
1469.759
|
0.8958
|
1342.746
|
109.9920
|
1119.984
|
161.786
|
884.9250
|
203.753
|
811.6043
|
31.4545
|
972.1739
|
|
12
|
134.7022
|
1471.634
|
12.8372
|
1343.984
|
94.5150
|
1120.33
|
143.116
|
884.8385
|
184.000
|
810.9424
|
45.2829
|
974.3861
|
|
13
|
147.6191
|
1473.641
|
26.5539
|
1345.378
|
78.8790
|
1120.769
|
123.916
|
884.8523
|
163.550
|
810.3641
|
59.0335
|
976.7316
|
|
14
|
160.4287
|
1475.767
|
40.2467
|
1346.915
|
63.0930
|
1121.295
|
104.216
|
884.9739
|
142.428
|
809.8916
|
72.7026
|
979.1822
|
|
15
|
173.1259
|
1478.001
|
53.9102
|
1348.583
|
47.1645
|
1121.902
|
84.044
|
885.2129
|
120.660
|
809.5491
|
86.2856
|
981.7078
|
|
16
|
185.7099
|
1480.331
|
67.5403
|
1350.371
|
31.0984
|
1122.585
|
63.431
|
885.5804
|
98.278
|
809.3627
|
99.7773
|
984.2767
|
|
17
|
198.1837
|
1482.743
|
81.1334
|
1352.268
|
14.8980
|
1123.338
|
42.404
|
886.0891
|
75.315
|
809.3590
|
113.1725
|
986.8570
|
|
18
|
210.5535
|
1485.224
|
94.6867
|
1354.265
|
1.4333
|
1124.158
|
20.994
|
886.7517
|
51.808
|
809.5640
|
126.4673
|
989.4174
|
|
19
|
222.8278
|
1487.757
|
108.1977
|
1356.350
|
17.8911
|
1125.040
|
0.769
|
887.5803
|
27.798
|
810.0020
|
139.6598
|
991.9286
|
|
20
|
235.0169
|
1490.325
|
121.6645
|
1358.513
|
34.4694
|
1125.979
|
22.855
|
888.5847
|
3.327
|
810.6936
|
152.7498
|
994.3636
|
|
21
|
247.1322
|
1492.907
|
135.0860
|
1360.738
|
51.1596
|
1126.972
|
45.232
|
889.7718
|
21.557
|
811.6552
|
165.7388
|
996.6990
|
|
22
|
259.1851
|
1495.481
|
148.4623
|
1363.009
|
67.9504
|
1128.010
|
67.868
|
891.1447
|
46.811
|
812.8972
|
178.6293
|
998.9143
|
|
23
|
271.1866
|
1498.022
|
161.7945
|
1365.305
|
84.8281
|
1129.083
|
90.730
|
892.7023
|
72.384
|
814.4236
|
191.4245
|
1000.9920
|
|
24
|
283.1469
|
1500.506
|
175.0846
|
1367.602
|
101.7767
|
1130.179
|
113.786
|
894.4395
|
98.228
|
816.2318
|
204.1278
|
1002.9180
|
|
25
|
295.0749
|
1502.905
|
188.3354
|
1369.872
|
118.7793
|
1131.283
|
137.003
|
896.3469
|
124.296
|
818.3120
|
216.7429
|
1004.6800
|
|
26
|
306.9781
|
1505.195
|
201.5501
|
1372.084
|
135.8182
|
1132.374
|
160.351
|
898.4120
|
150.543
|
820.6483
|
229.2738
|
1006.2670
|
|
27
|
318.8635
|
1507.350
|
214.7321
|
1374.207
|
152.8768
|
1133.433
|
183.801
|
900.6194
|
176.924
|
823.2191
|
241.7250
|
1007.6700
|
|
28
|
330.7369
|
1509.343
|
227.8844
|
1376.207
|
169.9397
|
1134.433
|
207.327
|
902.9514
|
203.398
|
825.9987
|
254.1017
|
1008.8810
|
|
29
|
342.6039
|
1511.150
|
241.0096
|
1378.052
|
186.9933
|
1135.350
|
230.903
|
905.3885
|
229.928
|
828.9584
|
266.4099
|
1009.8910
|
|
30
|
354.4694
|
1512.748
|
254.1096
|
1379.707
|
204.0269
|
1136.158
|
254.505
|
907.9105
|
256.478
|
832.0680
|
278.6570
|
1010.6930
|
|
31
|
366.3380
|
1514.117
|
267.1859
|
1381.145
|
221.0321
|
1136.831
|
278.110
|
910.4961
|
283.017
|
835.2977
|
290.8521
|
1011.2800
|
|
32
|
378.2137
|
1515.238
|
280.2396
|
1382.337
|
238.0038
|
1137.344
|
301.699
|
913.1249
|
309.516
|
838.6193
|
303.0058
|
1011.6470
|
|
33
|
390.1003
|
1516.097
|
293.2721
|
1383.259
|
254.9391
|
1137.677
|
325.249
|
915.7772
|
335.949
|
842.0071
|
315.1308
|
1011.7900
|
|
34
|
402.0008
|
1516.683
|
306.2855
|
1383.893
|
271.8378
|
1137.810
|
348.740
|
918.4351
|
362.290
|
845.4393
|
327.2408
|
1011.7050
|
|
35
|
413.9182
|
1516.986
|
319.2833
|
1384.222
|
288.7014
|
1137.729
|
372.151
|
921.0827
|
388.514
|
848.8983
|
339.3495
|
1011.3910
|
|
36
|
425.8549
|
1517.005
|
332.2706
|
1384.240
|
305.5328
|
1137.424
|
395.460
|
923.7070
|
414.599
|
852.3707
|
351.4696
|
1010.8470
|
|
37
|
437.8128
|
1516.737
|
345.2549
|
1383.941
|
322.3352
|
1136.889
|
418.643
|
926.2978
|
440.517
|
855.8474
|
363.6112
|
1010.0730
|
|
38
|
449.7935
|
1516.188
|
358.2454
|
1383.330
|
339.1115
|
1136.124
|
441.675
|
928.8475
|
466.242
|
859.3229
|
375.7819
|
1009.0720
|
|
39
|
461.7983
|
1515.364
|
371.2537
|
1382.416
|
355.8636
|
1135.134
|
464.529
|
931.3510
|
491.746
|
862.7949
|
387.9873
|
1007.8460
|
|
40
|
473.8288
|
1514.277
|
384.2926
|
1381.215
|
372.5915
|
1133.928
|
487.175
|
933.8054
|
516.996
|
866.2632
|
400.2315
|
1006.4040
|
|
41
|
485.8867
|
1512.942
|
397.3759
|
1379.749
|
389.2927
|
1132.521
|
509.583
|
936.2089
|
541.957
|
869.7286
|
412.5176
|
1004.7530
|
|
42
|
497.9743
|
1511.377
|
410.5173
|
1378.045
|
405.9619
|
1130.932
|
531.722
|
938.5610
|
566.592
|
873.1921
|
424.8483
|
1002.9080
|
|
43
|
510.0948
|
1509.607
|
423.7298
|
1376.137
|
422.5906
|
1129.184
|
553.559
|
940.8610
|
590.859
|
876.6538
|
437.2262
|
1000.8850
|
|
|
Frame Number
|
GT x
|
GT y
|
Knee x
|
Knee Y
|
Ankle x
|
Ankle y
|
R Heel x
|
R Heel Y
|
Met x
|
Met y
|
R Toe x
|
R Toe Y
|
Stride Events
|
|
–1
|
–151.9330
|
815.6667
|
60.0000
|
499.2000
|
179.6667
|
122.5333
|
137.0667
|
32.5333
|
318.8667
|
107.8000
|
389.6000
|
174.6000
|
|
0
|
–138.8750
|
817.3138
|
71.2735
|
500.1740
|
184.3008
|
122.2974
|
139.1965
|
33.7988
|
321.1163
|
101.7447
|
393.5727
|
166.1098
|
RTD
|
|
1
|
–127.3660
|
817.3990
|
81.5479
|
499.6656
|
188.6009
|
121.3638
|
140.9553
|
35.7224
|
324.5082
|
97.1523
|
399.1105
|
158.2565
|
|
2
|
–114.6950
|
817.6133
|
92.8275
|
499.2010
|
193.2326
|
120.3715
|
142.8490
|
37.7833
|
328.1142
|
92.1631
|
404.9800
|
149.7856
|
|
3
|
–101.2980
|
818.0074
|
104.7070
|
498.8362
|
197.9802
|
119.3710
|
144.7892
|
39.8826
|
331.7479
|
86.9928
|
410.8690
|
141.0844
|
|
4
|
–87.4525
|
818.6227
|
116.9140
|
498.6061
|
202.6871
|
118.3970
|
146.7124
|
41.9504
|
335.2787
|
81.8026
|
416.5578
|
132.4334
|
|
5
|
–73.3523
|
819.4881
|
129.2452
|
498.5237
|
207.2340
|
117.4741
|
148.5699
|
43.9356
|
338.6140
|
76.7251
|
421.8916
|
124.0495
|
|
6
|
–59.1365
|
820.6188
|
141.5343
|
498.5822
|
211.5301
|
116.6186
|
150.3248
|
45.8008
|
341.6912
|
71.8718
|
426.7681
|
116.1024
|
|
7
|
–44.9065
|
822.0160
|
153.6362
|
498.7572
|
215.5108
|
115.8410
|
151.9499
|
47.5205
|
344.4730
|
67.3340
|
431.1295
|
108.7213
|
|
8
|
–30.7351
|
823.6689
|
165.4220
|
499.0134
|
219.1348
|
115.1469
|
153.4265
|
49.0797
|
346.9431
|
63.1805
|
434.9549
|
101.9964
|
|
9
|
–16.6723
|
825.5570
|
176.7789
|
499.3102
|
222.3823
|
114.5388
|
154.7436
|
50.4725
|
349.1014
|
59.4569
|
438.2521
|
95.9820
|
|
10
|
–2.7509
|
827.6524
|
187.6139
|
499.6091
|
225.2517
|
114.0165
|
155.8960
|
51.7004
|
350.9600
|
56.1862
|
441.0497
|
90.6994
|
|
11
|
11.0093
|
829.9228
|
197.8582
|
499.8779
|
227.7565
|
113.5791
|
156.8838
|
52.7708
|
352.5393
|
53.3706
|
443.3898
|
86.1411
|
|
12
|
24.5970
|
832.3331
|
207.4701
|
500.0946
|
229.9220
|
113.2248
|
157.7112
|
53.6945
|
353.8654
|
50.9957
|
445.3221
|
82.2754
|
|
13
|
38.0060
|
834.8476
|
216.4356
|
500.2475
|
231.7811
|
112.9514
|
158.3862
|
54.4842
|
354.9672
|
49.0342
|
446.8991
|
79.0518
|
|
14
|
51.2330
|
837.4310
|
224.7652
|
500.3347
|
233.3704
|
112.7559
|
158.9206
|
55.1539
|
355.8746
|
47.4500
|
448.1728
|
76.4052
|
|
15
|
64.2766
|
840.0502
|
232.4894
|
500.3617
|
234.7272
|
112.6339
|
159.3292
|
55.7181
|
356.6170
|
46.2022
|
449.1921
|
74.2612
|
|
16
|
77.1368
|
842.6746
|
239.6519
|
500.3383
|
235.8862
|
112.5799
|
159.6301
|
56.1915
|
357.2221
|
45.2480
|
450.0017
|
72.5414
|
|
17
|
89.8161
|
845.2775
|
246.3037
|
500.2760
|
236.8787
|
112.5868
|
159.8431
|
56.5886
|
357.7151
|
44.5457
|
450.6412
|
71.1686
|
|
18
|
102.3196
|
847.8358
|
252.4979
|
500.1857
|
237.7323
|
112.6466
|
159.9886
|
56.9235
|
358.1183
|
44.0552
|
451.1447
|
70.0707
|
|
19
|
114.6559
|
850.3299
|
258.2861
|
500.0763
|
238.4710
|
112.7506
|
160.0858
|
57.2092
|
358.4507
|
43.7393
|
451.5414
|
69.1836
|
|
20
|
126.8370
|
852.7439
|
263.7166
|
499.9540
|
239.1157
|
112.8897
|
160.1514
|
57.4574
|
358.7282
|
43.5629
|
451.8558
|
68.4523
|
|
21
|
138.8776
|
855.0646
|
268.8339
|
499.8230
|
239.6849
|
113.0557
|
160.1989
|
57.6785
|
358.9634
|
43.4934
|
452.1079
|
67.8310
|
|
22
|
150.7940
|
857.2812
|
273.6783
|
499.6856
|
240.1949
|
113.2410
|
160.2386
|
57.8810
|
359.1665
|
43.5010
|
452.3141
|
67.2823
|
|
23
|
162.6026
|
859.3842
|
278.2859
|
499.5426
|
240.6593
|
113.4397
|
160.2780
|
58.0722
|
359.3451
|
43.5592
|
452.4875
|
66.7770
|
|
24
|
174.3181
|
861.3651
|
282.6890
|
499.3944
|
241.0892
|
113.6478
|
160.3224
|
58.2579
|
359.5049
|
43.6464
|
452.6383
|
66.2925
|
|
25
|
185.9522
|
863.2155
|
286.9158
|
499.2408
|
241.4929
|
113.8631
|
160.3755
|
58.4427
|
359.6502
|
43.7458
|
452.7746
|
65.8131
|
|
26
|
197.5134
|
864.9266
|
290.9908
|
499.0815
|
241.8764
|
114.0852
|
160.4402
|
58.6309
|
359.7843
|
43.8463
|
452.9024
|
65.3286
|
|
27
|
209.0071
|
866.4890
|
294.9362
|
498.9164
|
242.2435
|
114.3149
|
160.5187
|
58.8257
|
359.9092
|
43.9411
|
453.0261
|
64.8349
|
|
28
|
220.4373
|
867.8925
|
298.7722
|
498.7453
|
242.5968
|
114.5535
|
160.6126
|
59.0307
|
360.0264
|
44.0271
|
453.1489
|
64.3328
|
|
29
|
231.8087
|
869.1266
|
302.5183
|
498.5675
|
242.9386
|
114.8020
|
160.7236
|
59.2494
|
360.1368
|
44.1037
|
453.2730
|
63.8270
|
|
30
|
243.1287
|
870.1817
|
306.1950
|
498.3820
|
243.2710
|
115.0613
|
160.8529
|
59.4857
|
360.2404
|
44.1718
|
453.3998
|
63.3243
|
|
31
|
254.4073
|
871.0497
|
309.8237
|
498.1867
|
243.5966
|
115.3314
|
161.0014
|
59.7442
|
360.3372
|
44.2329
|
453.5304
|
62.8319
|
|
32
|
265.6574
|
871.7253
|
313.4281
|
497.9788
|
243.9186
|
115.6124
|
161.1695
|
60.0295
|
360.4265
|
44.2890
|
453.6651
|
62.3560
|
|
33
|
276.8928
|
872.2063
|
317.0341
|
497.7539
|
244.2404
|
115.9045
|
161.3575
|
60.3465
|
360.5074
|
44.3418
|
453.8039
|
61.9004
|
|
34
|
288.1276
|
872.4932
|
320.6698
|
497.5071
|
244.5661
|
116.2084
|
161.5659
|
60.7002
|
360.5789
|
44.3932
|
453.9465
|
61.4670
|
|
35
|
299.3745
|
872.5881
|
324.3649
|
497.2322
|
244.8999
|
116.5255
|
161.7948
|
61.0952
|
360.6402
|
44.4445
|
454.0924
|
61.0557
|
|
36
|
310.6444
|
872.4946
|
328.1502
|
496.9222
|
245.2467
|
116.8578
|
162.0449
|
61.5363
|
360.6906
|
44.4970
|
454.2406
|
60.6650
|
|
37
|
321.9457
|
872.2165
|
332.0572
|
496.5696
|
245.6118
|
117.2078
|
162.3167
|
62.0285
|
360.7300
|
44.5517
|
454.3904
|
60.2924
|
|
38
|
333.2847
|
871.7587
|
336.1172
|
496.1665
|
246.0014
|
117.5787
|
162.6114
|
62.5774
|
360.7588
|
44.6091
|
454.5409
|
59.9354
|
|
39
|
344.6653
|
871.1267
|
340.3614
|
495.7055
|
246.4221
|
117.9745
|
162.9301
|
63.1895
|
360.7782
|
44.6698
|
454.6915
|
59.5913
|
|
40
|
356.0901
|
870.3273
|
344.8206
|
495.1796
|
246.8816
|
118.4002
|
163.2748
|
63.8730
|
360.7903
|
44.7337
|
454.8418
|
59.2576
|
|
41
|
367.5610
|
869.3682
|
349.5252
|
494.5830
|
247.3890
|
118.8621
|
163.6482
|
64.6386
|
360.7982
|
44.8007
|
454.9916
|
58.9322
|
|
42
|
379.0804
|
868.2585
|
354.5053
|
493.9119
|
247.9545
|
119.3685
|
164.0544
|
65.4995
|
360.8056
|
44.8704
|
455.1414
|
58.6129
|
|
43
|
390.6524
|
867.0091
|
359.7906
|
493.1643
|
248.5902
|
119.9296
|
164.4993
|
66.4728
|
360.8171
|
44.9424
|
455.2919
|
58.2975
|
|
Frame Number
|
Head x
|
Head y
|
Shoulder x
|
Shoulder y
|
Elbow x
|
Elbow y
|
Wrist x
|
Wrist y
|
Hand x
|
Hand y
|
IC x
|
IC y
|
|
44
|
522.2518
|
1507.657
|
437.0246
|
1374.059
|
439.1667
|
1127.303
|
575.060
|
943.1083
|
614.715
|
880.1120
|
449.6549
|
998.7060
|
|
45
|
534.4501
|
1505.557
|
450.4108
|
1371.850
|
455.6750
|
1125.319
|
596.194
|
945.3013
|
638.117
|
883.5624
|
462.1389
|
996.3943
|
|
46
|
546.6946
|
1503.340
|
463.8944
|
1369.549
|
472.0967
|
1123.261
|
616.927
|
947.4374
|
661.022
|
886.9977
|
474.6841
|
993.9764
|
|
47
|
558.9905
|
1501.042
|
477.4785
|
1367.196
|
488.4105
|
1121.160
|
637.231
|
949.5129
|
683.390
|
890.4071
|
487.2987
|
991.4807
|
|
48
|
571.3426
|
1498.698
|
491.1625
|
1364.831
|
504.5930
|
1119.047
|
657.077
|
951.5224
|
705.182
|
893.7759
|
499.993
|
988.9370
|
|
49
|
583.7549
|
1496.348
|
504.9425
|
1362.491
|
520.6193
|
1116.949
|
676.440
|
953.4589
|
726.364
|
897.0853
|
512.7801
|
986.3754
|
|
50
|
596.2307
|
1494.029
|
518.8112
|
1360.212
|
536.4642
|
1114.896
|
695.298
|
955.3139
|
746.906
|
900.3132
|
525.6751
|
983.8261
|
|
51
|
608.7714
|
1491.778
|
532.7583
|
1358.027
|
552.1032
|
1112.913
|
713.631
|
957.0778
|
766.783
|
903.4340
|
538.6957
|
981.3188
|
|
52
|
621.3773
|
1489.633
|
546.7705
|
1355.967
|
567.5132
|
1111.025
|
731.424
|
958.7397
|
785.976
|
906.4198
|
551.8615
|
978.8828
|
|
53
|
634.0468
|
1487.627
|
560.8318
|
1354.057
|
582.6737
|
1109.255
|
748.666
|
960.2883
|
804.471
|
909.2411
|
565.1934
|
976.5466
|
|
54
|
646.7767
|
1485.791
|
574.9236
|
1352.324
|
597.5668
|
1107.623
|
765.348
|
961.7119
|
822.262
|
911.8676
|
578.7122
|
974.3387
|
|
55
|
659.5620
|
1484.151
|
589.0253
|
1350.788
|
612.1782
|
1106.150
|
781.463
|
962.9990
|
839.345
|
914.2688
|
592.4363
|
972.2856
|
|
56
|
672.3964
|
1482.731
|
603.1137
|
1349.467
|
626.4967
|
1104.854
|
797.011
|
964.1389
|
855.722
|
916.4159
|
606.3795
|
970.4116
|
|
57
|
685.2723
|
1481.550
|
617.1643
|
1348.376
|
640.5142
|
1103.749
|
811.991
|
965.1218
|
871.399
|
918.2821
|
620.5474
|
968.7373
|
|
58
|
698.1809
|
1480.623
|
631.1516
|
1347.527
|
654.2255
|
1102.850
|
826.407
|
965.9398
|
886.383
|
919.8438
|
634.9364
|
967.2792
|
|
59
|
711.1130
|
1479.962
|
645.0503
|
1346.926
|
667.6275
|
1102.164
|
840.264
|
966.5865
|
900.683
|
921.0807
|
649.5323
|
966.0490
|
|
60
|
724.0594
|
1479.574
|
658.8367
|
1346.579
|
680.7194
|
1101.697
|
853.568
|
967.0580
|
914.311
|
921.9768
|
664.3104
|
965.0532
|
|
61
|
737.0114
|
1479.463
|
672.4901
|
1346.484
|
693.5017
|
1101.452
|
866.329
|
967.3524
|
927.277
|
922.5203
|
679.2368
|
964.2941
|
|
62
|
749.9620
|
1479.627
|
685.9935
|
1346.638
|
705.9764
|
1101.426
|
878.554
|
967.4700
|
939.592
|
922.7038
|
694.2704
|
963.7690
|
|
63
|
762.9059
|
1480.060
|
699.3351
|
1347.032
|
718.1463
|
1101.611
|
890.255
|
967.4127
|
951.268
|
922.5244
|
709.3649
|
963.4708
|
|
64
|
775.8406
|
1480.750
|
712.5073
|
1347.654
|
730.0155
|
1101.999
|
901.441
|
967.1836
|
962.314
|
921.9839
|
724.4703
|
963.3876
|
|
65
|
788.7655
|
1481.681
|
725.5068
|
1348.486
|
741.5892
|
1102.574
|
912.121
|
966.7866
|
972.741
|
921.0883
|
739.5354
|
963.5039
|
|
66
|
801.6824
|
1482.833
|
738.3333
|
1349.510
|
752.8741
|
1103.321
|
922.308
|
966.2256
|
982.556
|
919.8477
|
754.5085
|
963.8010
|
|
67
|
814.5944
|
1484.184
|
750.9880
|
1350.703
|
763.8783
|
1104.220
|
932.011
|
965.5046
|
991.770
|
918.2762
|
769.3395
|
964.2584
|
|
68
|
827.5048
|
1485.710
|
763.4733
|
1352.042
|
774.6117
|
1105.254
|
941.240
|
964.6271
|
1000.388
|
916.3914
|
783.9819
|
964.8554
|
|
69
|
840.4169
|
1487.389
|
775.7909
|
1353.502
|
785.0856
|
1106.401
|
950.004
|
963.5969
|
1008.417
|
914.2144
|
798.3947
|
965.5728
|
|
70
|
853.3326
|
1489.199
|
787.9426
|
1355.059
|
795.3122
|
1107.645
|
958.312
|
962.4177
|
1015.865
|
911.7689
|
812.5442
|
966.3945
|
|
71
|
866.2526
|
1491.119
|
799.9299
|
1356.693
|
805.3045
|
1108.967
|
966.174
|
961.0942
|
1022.737
|
909.0815
|
826.4058
|
967.3087
|
|
72
|
879.1757
|
1493.128
|
811.7548
|
1358.382
|
815.0755
|
1110.353
|
973.597
|
959.6320
|
1029.043
|
906.1808
|
839.9639
|
968.3082
|
|
73
|
892.0995
|
1495.209
|
823.4208
|
1360.107
|
824.6380
|
1111.790
|
980.589
|
958.0385
|
1034.791
|
903.0973
|
853.2113
|
969.3906
|
|
74
|
905.0204
|
1497.344
|
834.9334
|
1361.852
|
834.0043
|
1113.264
|
987.157
|
956.3222
|
1039.989
|
899.8622
|
866.1494
|
970.5576
|
|
75
|
917.9341
|
1499.516
|
846.3014
|
1363.601
|
843.1862
|
1114.767
|
993.311
|
954.4936
|
1044.651
|
896.5072
|
878.7880
|
971.8138
|
|
76
|
930.8362
|
1501.708
|
857.5371
|
1365.343
|
852.1953
|
1116.289
|
999.058
|
952.5641
|
1048.789
|
893.0635
|
891.1464
|
973.1654
|
|
77
|
943.7226
|
1503.906
|
868.6569
|
1367.064
|
861.0429
|
1117.822
|
1004.410
|
950.5459
|
1052.419
|
889.5609
|
903.2537
|
974.6181
|
|
78
|
956.5902
|
1506.093
|
879.6808
|
1368.753
|
869.7412
|
1119.360
|
1009.377
|
948.4516
|
1055.557
|
886.0268
|
915.1477
|
976.1752
|
|
79
|
969.4370
|
1508.252
|
890.6320
|
1370.400
|
878.3033
|
1120.899
|
1013.972
|
946.2936
|
1058.223
|
882.4857
|
926.8735
|
977.8356
|
|
80
|
982.2618
|
1510.366
|
901.5361
|
1371.995
|
886.7441
|
1122.431
|
1018.210
|
944.0840
|
1060.436
|
878.9586
|
938.4812
|
979.5927
|
|
81
|
995.0647
|
1512.416
|
912.4197
|
1373.526
|
895.0804
|
1123.954
|
1022.109
|
941.8336
|
1062.220
|
875.4634
|
950.0233
|
981.4336
|
|
82
|
1007.8470
|
1514.380
|
923.3101
|
1374.984
|
903.3311
|
1125.462
|
1025.690
|
939.5526
|
1063.596
|
872.0145
|
961.5525
|
983.3398
|
|
83
|
1020.6090
|
1516.238
|
934.2332
|
1376.355
|
911.5175
|
1126.948
|
1028.974
|
937.2496
|
1064.591
|
868.6240
|
973.1191
|
985.2875
|
|
84
|
1033.3530
|
1517.966
|
945.2139
|
1377.627
|
919.6627
|
1128.403
|
1031.987
|
934.9323
|
1065.230
|
865.3018
|
984.7677
|
987.2489
|
|
85
|
1046.0810
|
1519.540
|
956.2747
|
1378.785
|
927.7914
|
1129.817
|
1034.758
|
932.6072
|
1065.541
|
862.0560
|
996.5345
|
989.1932
|
|
86
|
1058.7940
|
1520.939
|
967.4357
|
1379.812
|
935.9296
|
1131.176
|
1037.315
|
930.2805
|
1065.556
|
858.8937
|
1008.4450
|
991.0879
|
|
87
|
1071.4940
|
1522.141
|
978.7147
|
1380.693
|
944.1037
|
1132.463
|
1039.691
|
927.9574
|
1065.307
|
855.8212
|
1020.5140
|
992.8999
|
|
88
|
1084.1810
|
1523.124
|
990.1266
|
1381.411
|
952.3407
|
1133.663
|
1041.920
|
925.6434
|
1064.830
|
852.8441
|
1032.7460
|
994.5969
|
|
89
|
1096.8570
|
1523.870
|
1001.6840
|
1381.949
|
960.6672
|
1134.758
|
1044.036
|
923.3441
|
1064.163
|
849.9679
|
1045.1340
|
996.1484
|
|
90
|
1109.5220
|
1524.363
|
1013.3960
|
1382.293
|
969.1091
|
1135.730
|
1046.076
|
921.0654
|
1063.349
|
847.1981
|
1057.6670
|
997.5264
|
|
|
Frame Number
|
GT x
|
GT y
|
Knee x
|
Knee y
|
Ankle x
|
Ankle y
|
R Heel x
|
R Heel y
|
Met x
|
Met y
|
R Toe x
|
R Toe y
|
Stride Events
|
|
44
|
402.2833
|
865.6323
|
365.4101
|
492.3406
|
249.3104
|
120.5581
|
164.9916
|
67.5794
|
360.8379
|
45.0161
|
455.4447
|
57.9836
|
|
|
45
|
413.9826
|
864.1425
|
371.3921
|
491.4435
|
250.1318
|
121.2689
|
165.5426
|
68.8445
|
360.8736
|
45.0907
|
455.6017
|
57.6685
|
|
46
|
425.7624
|
862.5563
|
377.7643
|
490.4779
|
251.0741
|
122.0795
|
166.1676
|
70.2976
|
360.9301
|
45.1652
|
455.7655
|
57.3491
|
|
47
|
437.6376
|
860.8923
|
384.5530
|
489.4505
|
252.1602
|
123.0099
|
166.8858
|
71.9725
|
361.0138
|
45.2383
|
455.9388
|
57.0217
|
|
48
|
449.6248
|
859.1707
|
391.7842
|
488.3699
|
253.4165
|
124.0820
|
167.7211
|
73.9066
|
361.1312
|
45.3084
|
456.1251
|
56.6824
|
|
49
|
461.7424
|
857.4121
|
399.4829
|
487.2455
|
254.8731
|
125.3197
|
168.7025
|
76.1405
|
361.2889
|
45.3743
|
456.3279
|
56.3267
|
|
50
|
474.0093
|
855.6371
|
407.6740
|
486.0878
|
256.5635
|
126.7479
|
169.8648
|
78.7167
|
361.4933
|
45.4355
|
456.5518
|
55.9497
|
|
51
|
486.4451
|
853.8651
|
416.3824
|
484.9072
|
258.5252
|
128.3919
|
171.2490
|
81.6790
|
361.7507
|
45.4938
|
456.8016
|
55.5460
|
|
52
|
499.0691
|
852.1139
|
425.6334
|
483.7140
|
260.7993
|
130.2768
|
172.9024
|
85.0714
|
362.0677
|
45.5543
|
457.0836
|
55.1095
|
|
53
|
511.9001
|
850.3997
|
435.4529
|
482.5174
|
263.4308
|
132.4263
|
174.8798
|
88.9365
|
362.4523
|
45.6266
|
457.4059
|
54.6334
|
|
54
|
524.9558
|
848.7370
|
445.8680
|
481.3257
|
266.4682
|
134.8621
|
177.2433
|
93.3147
|
362.9149
|
45.7260
|
457.7787
|
54.1101
|
|
55
|
538.2520
|
847.1390
|
456.9072
|
480.1456
|
269.9636
|
137.6026
|
180.0630
|
98.2425
|
363.4703
|
45.8735
|
458.2149
|
53.5311
|
|
56
|
551.8018
|
845.6168
|
468.6003
|
478.9818
|
273.9725
|
140.6631
|
183.4173
|
103.7511
|
364.1388
|
46.0956
|
458.7312
|
52.8864
|
|
57
|
565.6142
|
844.1796
|
480.9787
|
477.8369
|
278.5537
|
144.0548
|
187.3924
|
109.8648
|
364.9479
|
46.4237
|
459.3485
|
52.1647
|
|
58
|
579.6932
|
842.8347
|
494.0746
|
476.7118
|
283.7696
|
147.7851
|
192.0818
|
116.5996
|
365.9339
|
46.8940
|
460.0931
|
51.3535
|
|
59
|
594.0364
|
841.5867
|
507.9210
|
475.6049
|
289.6859
|
151.8575
|
197.5852
|
123.9614
|
367.1434
|
47.5465
|
460.9979
|
50.4391
|
LTD
|
|
60
|
608.6337
|
840.4378
|
522.5499
|
474.5135
|
296.3716
|
156.2711
|
204.0059
|
131.9451
|
368.6348
|
48.4256
|
462.1044
|
49.4077
|
|
61
|
623.4672
|
839.3875
|
537.9915
|
473.4333
|
303.8978
|
161.0196
|
211.4477
|
140.5324
|
370.4799
|
49.5791
|
463.4636
|
48.2472
|
|
62
|
638.5101
|
838.4326
|
554.2720
|
472.3594
|
312.3368
|
166.0903
|
220.0112
|
149.6902
|
372.7646
|
51.0562
|
465.1384
|
46.9498
|
|
63
|
653.7275
|
837.5678
|
571.4115
|
471.2875
|
321.7593
|
171.4627
|
229.7893
|
159.3682
|
375.5898
|
52.9052
|
467.2046
|
45.5158
|
|
64
|
669.0768
|
836.7864
|
589.4216
|
470.2143
|
332.2322
|
177.1082
|
240.8623
|
169.4967
|
379.0706
|
55.1688
|
469.7528
|
43.9582
|
|
65
|
684.5092
|
836.0806
|
608.3036
|
469.1397
|
343.8152
|
182.9895
|
253.2933
|
179.9845
|
383.3353
|
57.8796
|
472.8908
|
42.3077
|
|
66
|
699.9719
|
835.4432
|
628.0463
|
468.0684
|
356.5576
|
189.0610
|
267.1239
|
190.7183
|
388.5238
|
61.0557
|
476.7449
|
40.6152
|
|
67
|
715.4105
|
834.8681
|
648.6252
|
467.0117
|
370.4949
|
195.2689
|
282.3695
|
201.5629
|
394.7855
|
64.6967
|
481.4629
|
38.9541
|
|
68
|
730.7715
|
834.3520
|
670.0022
|
465.9895
|
385.6464
|
201.5527
|
299.0160
|
212.3643
|
402.2761
|
68.7818
|
487.2153
|
37.4164
|
|
69
|
746.0055
|
833.8949
|
692.1253
|
465.0319
|
402.0134
|
207.8452
|
317.0172
|
222.9540
|
411.1545
|
73.2680
|
494.1952
|
36.1063
|
|
70
|
761.0693
|
833.5012
|
714.9302
|
464.1787
|
419.5800
|
214.0742
|
336.2964
|
233.1561
|
421.5793
|
78.0903
|
502.6152
|
35.1289
|
|
71
|
775.9278
|
833.1797
|
738.3418
|
463.4794
|
438.3152
|
220.1630
|
356.7498
|
242.7956
|
433.7019
|
83.1627
|
512.6991
|
34.5766
|
|
72
|
790.5556
|
832.9440
|
762.2759
|
462.9903
|
458.1768
|
226.0319
|
378.2556
|
251.7072
|
447.6596
|
88.3795
|
524.6682
|
34.5153
|
|
73
|
804.9377
|
832.8115
|
786.6420
|
462.7713
|
479.1165
|
231.5979
|
400.6838
|
259.7432
|
463.5649
|
93.6183
|
538.7225
|
34.9722
|
|
74
|
819.0697
|
832.8028
|
811.3455
|
462.8813
|
501.0830
|
236.7762
|
423.9086
|
266.7791
|
481.4957
|
98.7442
|
555.0212
|
35.9293
|
|
75
|
832.9578
|
832.9400
|
836.2902
|
463.3738
|
524.0245
|
241.4812
|
447.8179
|
272.7165
|
501.4864
|
103.6165
|
573.6661
|
37.3241
|
|
76
|
846.6178
|
833.2444
|
861.3812
|
464.2920
|
547.8890
|
245.6286
|
472.3199
|
277.4831
|
523.5240
|
108.0956
|
594.6932
|
39.0584
|
RTO
|
|
77
|
860.0739
|
833.7345
|
886.5270
|
465.6647
|
572.6235
|
249.1396
|
497.3450
|
281.0300
|
547.5494
|
112.0514
|
618.0732
|
41.0124
|
|
78
|
873.3571
|
834.4230
|
911.6413
|
467.5040
|
598.1741
|
251.9441
|
522.8448
|
283.3286
|
573.4650
|
115.3715
|
643.7214
|
43.0613
|
|
79
|
886.5038
|
835.3152
|
936.6445
|
469.8040
|
624.4861
|
253.9848
|
548.7892
|
284.3665
|
601.1465
|
117.9675
|
671.5116
|
45.0897
|
|
80
|
899.5530
|
836.4076
|
961.4648
|
472.5408
|
651.5061
|
255.2193
|
575.1624
|
284.1450
|
630.4558
|
119.7792
|
701.2915
|
47.0030
|
|
81
|
912.5449
|
837.6876
|
986.0383
|
475.6746
|
679.1844
|
255.6219
|
601.9611
|
282.6769
|
661.2527
|
120.7769
|
732.8957
|
48.7337
|
|
82
|
925.5189
|
839.1341
|
1010.3090
|
479.1515
|
707.4776
|
255.1832
|
629.1921
|
279.9857
|
693.4044
|
120.9621
|
766.1557
|
50.2438
|
|
83
|
938.5117
|
840.7193
|
1034.2300
|
482.9071
|
736.3500
|
253.9097
|
656.8714
|
276.1059
|
726.7898
|
120.3650
|
800.9062
|
51.5241
|
|
84
|
951.5555
|
842.4100
|
1057.7600
|
486.8694
|
765.7741
|
251.8223
|
685.0226
|
271.0822
|
761.3018
|
119.0424
|
836.9882
|
52.5912
|
|
85
|
964.6761
|
844.1692
|
1080.8670
|
490.9622
|
795.7294
|
248.9548
|
713.6750
|
264.9703
|
796.8452
|
117.0729
|
874.2502
|
53.4839
|
|
86
|
977.8912
|
845.9573
|
1103.5240
|
495.1083
|
826.2008
|
245.3527
|
742.8620
|
257.8366
|
833.3345
|
114.5524
|
912.5479
|
54.2587
|
|
87
|
991.2104
|
847.7333
|
1125.7100
|
499.2321
|
857.1769
|
241.0716
|
772.6188
|
249.7584
|
870.6895
|
111.5892
|
951.7430
|
54.9853
|
|
88
|
1004.6350
|
849.4551
|
1147.4090
|
503.2616
|
888.6476
|
236.1757
|
802.9806
|
240.8236
|
908.8328
|
108.2993
|
991.7024
|
55.7423
|
|
89
|
1018.1610
|
851.0812
|
1168.6090
|
507.1302
|
920.6024
|
230.7369
|
833.9800
|
231.1305
|
947.6873
|
104.8021
|
1032.2970
|
56.6135
|
|
90
|
1031.7800
|
852.5717
|
1189.3010
|
510.7773
|
953.0286
|
224.8342
|
865.6452
|
220.7872
|
987.1745
|
101.2173
|
1073.4010
|
57.6847
|
|
Frame Number
|
Head x
|
Head y
|
Shoulder x
|
Shoulder y
|
Elbow x
|
Elbow y
|
Wrist x
|
Wrist y
|
Hand x
|
Hand y
|
IC x
|
IC y
|
|
91
|
1122.1780
|
1524.589
|
1025.2720
|
1382.429
|
977.6909
|
1136.564
|
1048.081
|
918.8136
|
1062.432
|
844.5402
|
1070.3300
|
998.7059
|
|
92
|
1134.8250
|
1524.536
|
1037.3170
|
1382.347
|
986.4352
|
1137.245
|
1050.090
|
916.5961
|
1061.459
|
842.0001
|
1083.1050
|
999.6655
|
|
93
|
1147.4650
|
1524.197
|
1049.5320
|
1382.041
|
995.3621
|
1137.763
|
1052.148
|
914.4208
|
1060.479
|
839.5836
|
1095.9770
|
1000.3870
|
|
94
|
1160.1020
|
1523.572
|
1061.9210
|
1381.507
|
1004.4890
|
1138.108
|
1054.301
|
912.2968
|
1059.545
|
837.2960
|
1108.9330
|
1000.8560
|
|
95
|
1172.7400
|
1522.661
|
1074.4800
|
1380.745
|
1013.8300
|
1138.275
|
1056.598
|
910.2335
|
1058.710
|
835.1422
|
1121.9610
|
1001.0630
|
|
96
|
1185.3860
|
1521.474
|
1087.2070
|
1379.759
|
1023.3960
|
1138.259
|
1059.087
|
908.2402
|
1058.030
|
833.1259
|
1135.0540
|
1000.9990
|
|
97
|
1198.0500
|
1520.024
|
1100.0940
|
1378.556
|
1033.1920
|
1138.063
|
1061.813
|
906.3257
|
1057.559
|
831.2495
|
1148.2070
|
1000.6620
|
|
98
|
1210.7410
|
1518.332
|
1113.1330
|
1377.149
|
1043.2210
|
1137.688
|
1064.820
|
904.4973
|
1057.355
|
829.5134
|
1161.4160
|
1000.0520
|
|
99
|
1223.4720
|
1516.420
|
1126.3120
|
1375.550
|
1053.4790
|
1137.144
|
1068.144
|
902.7599
|
1057.472
|
827.9161
|
1174.6800
|
999.1736
|
|
100
|
1236.2490
|
1514.314
|
1139.6170
|
1373.776
|
1063.9570
|
1136.441
|
1071.818
|
901.1171
|
1057.963
|
826.4537
|
1187.9990
|
998.0358
|
|
101
|
1249.0780
|
1512.043
|
1153.0310
|
1371.846
|
1074.6410
|
1135.594
|
1075.871
|
899.5702
|
1058.880
|
825.1201
|
1201.3720
|
996.6514
|
|
102
|
1261.9590
|
1509.631
|
1166.5340
|
1369.781
|
1085.5120
|
1134.623
|
1080.325
|
898.1190
|
1060.268
|
823.9072
|
1214.7950
|
995.0374
|
|
103
|
1274.8870
|
1507.109
|
1180.1040
|
1367.603
|
1096.5420
|
1133.550
|
1085.200
|
896.7623
|
1062.169
|
822.8048
|
1228.2650
|
993.2150
|
|
104
|
1287.8500
|
1504.502
|
1193.7160
|
1365.336
|
1107.7010
|
1132.399
|
1090.508
|
895.4979
|
1064.614
|
821.8015
|
1241.7710
|
991.2089
|
|
105
|
1300.8320
|
1501.839
|
1207.3390
|
1363.007
|
1118.9540
|
1131.197
|
1096.251
|
894.3228
|
1067.629
|
820.8849
|
1255.2970
|
989.0475
|
|
106
|
1313.8080
|
1499.151
|
1220.9350
|
1360.641
|
1130.2590
|
1129.969
|
1102.426
|
893.2339
|
1071.225
|
820.0424
|
1268.8180
|
986.7625
|
|
107
|
1326.7450
|
1496.467
|
1234.4590
|
1358.266
|
1141.5710
|
1128.740
|
1109.012
|
892.2280
|
1075.401
|
819.2618
|
1282.3000
|
984.3880
|
|
108
|
1339.5990
|
1493.820
|
1247.8540
|
1355.909
|
1152.8390
|
1127.533
|
1115.977
|
891.3019
|
1080.135
|
818.5322
|
1295.6950
|
981.9608
|
|
109
|
1352.3100
|
1491.240
|
1261.0510
|
1353.599
|
1164.0020
|
1126.369
|
1123.268
|
890.4531
|
1085.389
|
817.8444
|
1308.9420
|
979.5194
|
|
110
|
1364.8020
|
1488.760
|
1273.9640
|
1351.363
|
1174.9900
|
1125.264
|
1130.814
|
889.6794
|
1091.097
|
817.1916
|
1321.9620
|
977.1038
|
|
111
|
1376.9790
|
1486.412
|
1286.4910
|
1349.228
|
1185.7180
|
1124.232
|
1138.519
|
888.9791
|
1097.170
|
816.5699
|
1334.6530
|
974.7546
|
|
112
|
1388.7200
|
1484.224
|
1298.5100
|
1347.222
|
1196.0800
|
1123.284
|
1146.261
|
888.3509
|
1103.487
|
815.9788
|
1346.8920
|
972.5130
|
|
113
|
1399.8780
|
1482.223
|
1309.8780
|
1345.372
|
1205.9500
|
1122.428
|
1153.894
|
887.7934
|
1109.898
|
815.4207
|
1358.5280
|
970.4190
|
|
114
|
1410.2790
|
1480.435
|
1320.4330
|
1343.704
|
1215.1790
|
1121.670
|
1161.243
|
887.3054
|
1116.221
|
814.9016
|
1369.3830
|
968.5109
|
|
115
|
1419.7300
|
1478.880
|
1329.9900
|
1342.240
|
1223.5910
|
1121.013
|
1168.110
|
886.8860
|
1122.249
|
814.4294
|
1379.2550
|
966.8234
|
|
116
|
1428.0220
|
1477.574
|
1338.3540
|
1341.002
|
1231.0000
|
1120.463
|
1174.283
|
886.5345
|
1127.759
|
814.0141
|
1387.9280
|
965.3857
|
|
117
|
1434.9580
|
1476.527
|
1345.3370
|
1340.002
|
1237.2200
|
1120.020
|
1179.554
|
886.2509
|
1132.526
|
813.6654
|
1395.1920
|
964.2192
|
|
118
|
1440.3830
|
1475.740
|
1350.7930
|
1339.246
|
1242.1030
|
1119.685
|
1183.750
|
886.0347
|
1136.362
|
813.3915
|
1400.8820
|
963.3334
|
|
119
|
1444.2530
|
1475.199
|
1354.6820
|
1338.724
|
1245.6000
|
1119.453
|
1186.789
|
885.8832
|
1139.165
|
813.1953
|
1404.9460
|
962.7195
|
|
120
|
1446.7480
|
1474.865
|
1357.1890
|
1338.399
|
1247.8630
|
1119.307
|
1188.778
|
885.7864
|
1141.016
|
813.0679
|
1407.5700
|
962.3362
|
|
121
|
1448.4950
|
1474.645
|
1358.9430
|
1338.183
|
1249.4580
|
1119.209
|
1190.200
|
885.7190
|
1142.352
|
812.9777
|
1409.4110
|
962.0807
|
|
122
|
1535.0000
|
1468.600
|
1446.2670
|
1331.267
|
1332.6670
|
1115.000
|
1271.000
|
881.6667
|
1222.533
|
807.7334
|
1503.2670
|
954.0667
|
|
Frame Number
|
GT x
|
GT y
|
Knee X
|
Knee y
|
Ankle x
|
Ankle Y
|
R Heel x
|
R Heel y
|
Met x
|
Met y
|
R Toe x
|
R Toe y
|
Stride Events
|
|
91
|
1045.4800
|
853.8901
|
1209.4790
|
514.1490
|
985.9099
|
218.5530
|
897.9977
|
209.9099
|
1027.2140
|
97.6617
|
1114.8910
|
59.0417
|
|
|
92
|
1059.2530
|
855.0042
|
1229.1370
|
517.1985
|
1019.2250
|
211.9852
|
931.0504
|
198.6207
|
1067.7200
|
94.2472
|
1156.6450
|
60.7684
|
|
93
|
1073.0900
|
855.8873
|
1248.2710
|
519.8859
|
1052.9450
|
205.2283
|
964.8050
|
187.0457
|
1108.6050
|
91.0794
|
1198.5420
|
62.9454
|
|
94
|
1086.9820
|
856.5187
|
1266.8780
|
522.1782
|
1087.0360
|
198.3838
|
999.2498
|
175.3125
|
1149.7730
|
88.2566
|
1240.4600
|
65.6477
|
|
95
|
1100.9190
|
856.8826
|
1284.9580
|
524.0499
|
1121.4520
|
191.5556
|
1034.3570
|
163.5488
|
1191.1220
|
85.8689
|
1282.2760
|
68.9418
|
|
96
|
1114.8900
|
856.9678
|
1302.5100
|
525.4825
|
1156.1350
|
184.8474
|
1070.0800
|
151.8817
|
1232.5400
|
83.9973
|
1323.8630
|
72.8823
|
|
97
|
1128.8790
|
856.7668
|
1319.5380
|
526.4650
|
1191.0160
|
178.3600
|
1106.3500
|
140.4368
|
1273.9020
|
82.7122
|
1365.0880
|
77.5078
|
|
98
|
1142.8670
|
856.2758
|
1336.0510
|
526.9944
|
1226.0050
|
172.1887
|
1143.0730
|
129.3379
|
1315.0730
|
82.0706
|
1405.8150
|
82.8383
|
|
99
|
1156.8330
|
855.4942
|
1352.0600
|
527.0763
|
1260.9970
|
166.4202
|
1180.1300
|
118.7044
|
1355.9030
|
82.1127
|
1445.9060
|
88.8720
|
|
100
|
1170.7550
|
854.4260
|
1367.5830
|
526.7247
|
1295.8660
|
161.1292
|
1217.3720
|
108.6481
|
1396.2270
|
82.8590
|
1485.2190
|
95.5835
|
|
101
|
1184.6140
|
853.0799
|
1382.6470
|
525.9632
|
1330.4660
|
156.3753
|
1254.6250
|
99.2689
|
1435.8710
|
84.3064
|
1523.6130
|
102.9216
|
|
102
|
1198.3950
|
851.4703
|
1397.2810
|
524.8242
|
1364.6330
|
152.1993
|
1291.6890
|
90.6500
|
1474.6500
|
86.4260
|
1560.9450
|
110.8074
|
|
103
|
1212.0860
|
849.6176
|
1411.5220
|
523.3494
|
1398.1890
|
148.6200
|
1328.3410
|
82.8528
|
1512.3730
|
89.1621
|
1597.0790
|
119.1344
|
|
104
|
1225.6780
|
847.5482
|
1425.4110
|
521.5883
|
1430.9430
|
145.6326
|
1364.3410
|
75.9138
|
1548.8460
|
92.4315
|
1631.8780
|
127.7686
|
|
105
|
1239.1620
|
845.2944
|
1438.9880
|
519.5977
|
1462.7010
|
143.2082
|
1399.4320
|
69.8418
|
1583.8800
|
96.1250
|
1665.2140
|
136.5525
|
|
106
|
1252.5260
|
842.8939
|
1452.2900
|
517.4393
|
1493.2680
|
141.2944
|
1433.3560
|
64.6175
|
1617.2900
|
100.1100
|
1696.9680
|
145.3103
|
|
107
|
1265.7520
|
840.3885
|
1465.3500
|
515.1776
|
1522.4550
|
139.8191
|
1465.8530
|
60.1938
|
1648.9040
|
104.2365
|
1727.0330
|
153.8557
|
|
108
|
1278.8090
|
837.8237
|
1478.1860
|
512.8766
|
1550.0890
|
138.6949
|
1496.6760
|
56.4992
|
1678.5610
|
108.3453
|
1755.3130
|
162.0012
|
|
109
|
1291.6520
|
835.2469
|
1490.7990
|
510.5973
|
1576.0100
|
137.8264
|
1525.5960
|
53.4431
|
1706.1190
|
112.2787
|
1781.7270
|
169.5697
|
|
110
|
1304.2180
|
832.7062
|
1503.1670
|
508.3945
|
1600.0780
|
137.1185
|
1552.4090
|
50.9230
|
1731.4590
|
115.8918
|
1806.2040
|
176.4070
|
|
111
|
1316.4240
|
830.2491
|
1515.2380
|
506.3149
|
1622.1730
|
136.4850
|
1576.9420
|
48.8343
|
1754.4840
|
119.0627
|
1828.6820
|
182.3930
|
|
112
|
1328.1590
|
827.9207
|
1526.9250
|
504.3956
|
1642.1950
|
135.8571
|
1599.0540
|
47.0793
|
1775.1250
|
121.7017
|
1849.1040
|
187.4518
|
|
113
|
1339.2880
|
825.7624
|
1538.1000
|
502.6643
|
1660.0600
|
135.1893
|
1618.6440
|
45.5762
|
1793.3400
|
123.7588
|
1867.4180
|
191.5581
|
|
114
|
1349.6500
|
823.8110
|
1548.5950
|
501.1398
|
1675.7030
|
134.4637
|
1635.6440
|
44.2660
|
1809.1160
|
125.2282
|
1883.5680
|
194.7383
|
|
115
|
1359.0580
|
822.0975
|
1558.2070
|
499.8333
|
1689.0760
|
133.6909
|
1650.0260
|
43.1152
|
1822.4670
|
126.1492
|
1897.5000
|
197.0671
|
|
116
|
1367.3130
|
820.6466
|
1566.7050
|
498.7500
|
1700.1520
|
132.9067
|
1661.8020
|
42.1148
|
1833.4310
|
126.6039
|
1909.1600
|
198.6590
|
|
117
|
1374.2220
|
819.4747
|
1573.8630
|
497.8898
|
1708.9330
|
132.1643
|
1671.0280
|
41.2741
|
1842.0700
|
126.7078
|
1918.5100
|
199.6550
|
|
118
|
1379.6320
|
818.5875
|
1579.4960
|
497.2469
|
1715.4760
|
131.5218
|
1677.8230
|
40.6102
|
1848.4840
|
126.5941
|
1925.5590
|
200.2064
|
|
119
|
1383.4960
|
817.9734
|
1583.5340
|
496.8057
|
1719.9390
|
131.0243
|
1682.4070
|
40.1330
|
1852.8560
|
126.3889
|
1930.4270
|
200.4570
|
|
120
|
1385.9930
|
817.5894
|
1586.1500
|
496.5313
|
1722.6820
|
130.6790
|
1685.1930
|
39.8256
|
1855.5500
|
126.1770
|
1933.4640
|
200.5254
|
|
121
|
1387.7470
|
817.3316
|
1587.9920
|
496.3473
|
1724.4700
|
130.4152
|
1686.9810
|
39.6145
|
1857.3240
|
125.9547
|
1935.4950
|
200.4826
|
RTD
|
|
122
|
1483.7330
|
808.6667
|
1679.0000
|
487.2667
|
1780.3330
|
116.5333
|
1731.2670
|
38.6666
|
1917.8670
|
95.6666
|
1937.5250
|
200.4398
|
|
P.478
|
TABLE C-2 Kinetic Data in Newtons
|
|
Number
|
Fx
|
Fy
|
Fz
|
Events
|
|
1
|
0
|
0
|
0
|
|
|
0
|
1.5647
|
0.2007
|
7.04480
|
RTD
|
|
1
|
1.2618
|
6.1802
|
53.34734
|
|
2
|
1.7255
|
9.5325
|
111.1378
|
|
3
|
9.4928
|
4.6627
|
184.3624
|
|
4
|
21.0518
|
22.5572
|
235.4881
|
|
5
|
28.9799
|
41.3995
|
289.6832
|
|
6
|
30.0140
|
54.5544
|
335.5472
|
|
7
|
26.0155
|
66.6458
|
385.7960
|
|
8
|
18.2023
|
73.6048
|
427.9769
|
|
9
|
10.7337
|
82.5751
|
459.7222
|
|
10
|
6.8501
|
85.7424
|
485.8550
|
|
11
|
5.7930
|
89.8577
|
499.7984
|
|
12
|
1.3808
|
89.5803
|
520.2312
|
|
13
|
5.6510
|
93.1406
|
529.8775
|
|
14
|
14.5903
|
92.2852
|
545.6625
|
|
15
|
19.1174
|
89.9271
|
544.9609
|
|
16
|
25.3220
|
88.2393
|
555.5719
|
|
17
|
26.9306
|
82.4133
|
549.9595
|
|
18
|
28.0796
|
76.7952
|
553.0288
|
|
19
|
25.8505
|
68.7728
|
540.5762
|
|
20
|
24.7705
|
62.7387
|
533.2099
|
|
21
|
22.6563
|
54.2539
|
514.1803
|
|
22
|
21.1166
|
49.3988
|
496.4661
|
|
23
|
19.6229
|
42.0237
|
474.8933
|
|
24
|
17.8075
|
38.0703
|
444.9019
|
|
25
|
17.2790
|
31.8743
|
428.5030
|
|
26
|
16.0840
|
28.5682
|
397.5470
|
|
27
|
17.3019
|
23.9212
|
382.2882
|
|
28
|
15.6474
|
21.3319
|
356.4184
|
|
29
|
16.3138
|
19.1818
|
341.4227
|
|
30
|
14.5214
|
17.2860
|
316.2545
|
|
31
|
14.2226
|
16.3843
|
310.0282
|
|
32
|
11.9476
|
14.4423
|
290.2970
|
|
33
|
11.2352
|
14.4885
|
288.2801
|
|
34
|
9.9023
|
12.8933
|
275.9152
|
|
35
|
9.6495
|
13.1014
|
275.0382
|
|
36
|
9.5346
|
10.3964
|
269.6889
|
|
37
|
9.4657
|
11.1593
|
271.7935
|
|
38
|
10.2700
|
7.5758
|
273.8105
|
|
39
|
10.7067
|
7.1134
|
275.6521
|
|
40
|
12.2693
|
3.5299
|
285.8246
|
|
41
|
12.0855
|
2.9519
|
288.7185
|
|
42
|
13.0966
|
0.4550
|
303.9773
|
|
43
|
13.0047
|
1.9262
|
313.3606
|
|
44
|
14.2915
|
5.1167
|
336.9503
|
|
45
|
12.2693
|
9.0932
|
351.0691
|
|
46
|
13.0966
|
12.9773
|
379.3943
|
|
47
|
12.4531
|
18.4103
|
396.6701
|
|
48
|
14.4984
|
22.5949
|
428.9415
|
|
49
|
14.9120
|
29.7157
|
451.6543
|
|
50
|
15.9921
|
34.6401
|
482.5227
|
|
51
|
16.8883
|
43.2636
|
508.2171
|
|
52
|
18.2211
|
48.9741
|
533.8238
|
|
53
|
20.1745
|
57.4127
|
558.2904
|
|
54
|
21.4843
|
63.2157
|
574.0754
|
|
55
|
23.7823
|
71.7005
|
592.9296
|
|
56
|
24.4717
|
78.2664
|
600.9098
|
|
57
|
26.5399
|
85.8033
|
610.5562
|
|
58
|
24.8624
|
93.0165
|
604.5930
|
|
59
|
24.8624
|
98.9813
|
604.4176
|
|
60
|
22.2427
|
104.5069
|
583.8094
|
|
61
|
20.4043
|
107.3506
|
570.0415
|
|
62
|
17.0032
|
110.4948
|
535.1392
|
|
63
|
14.2686
|
110.7029
|
503.3062
|
|
64
|
9.7185
|
109.1077
|
452.5313
|
|
65
|
6.2944
|
101.1315
|
404.6502
|
|
66
|
3.8356
|
91.2132
|
345.5443
|
|
67
|
3.1002
|
77.4110
|
285.2985
|
|
68
|
3.6287
|
66.4524
|
228.9111
|
|
69
|
3.0542
|
51.3323
|
171.8222
|
|
70
|
4.2952
|
39.7495
|
128.9397
|
|
71
|
4.4330
|
26.8258
|
88.1619
|
|
72
|
4.6399
|
18.1560
|
61.6782
|
|
73
|
2.3648
|
10.2261
|
34.0546
|
|
74
|
2.0431
|
5.3710
|
25.1975
|
|
75
|
0.0480
|
2.8972
|
9.3248
|
|
76
|
1.4916
|
0.9089
|
10.99105
|
RTO
|
|
P.479
Appendix D: Numerical Example for Calculating Projectile Motion
The equations of constant acceleration all use parameters that are basic to linear kinematics. The three equations of constant acceleration thus provide a useful method of analyzing projectile motion. Suppose a shot putter releases the shot at an angle of 40° from a height of 2.2 m with a velocity of 13.3 m/s. Figure 8-41 illustrates what is known about the conditions of the projectile at the instant of projection and the shape of the trajectory based on our previous discussion.
The problem can be solved in seven steps using the equations of constant acceleration. Remember: To find the range of a projectile, the horizontal velocity and the length of time that the shot was in the air must be known.
Step 1
Calculate the initial vertical and horizontal velocities. (Use Appendix C for sine and cosine values).
Step 2
Use the first equation of constant acceleration to calculate the time required for the projectile to reach the apex of its trajectory. Because it is necessary to calculate the time to the apex, the equation using the vertical velocity must be used. Thus, the acceleration due to gravity, a, will act, bringing the vertical velocity to zero at the apex.
P.480
Step 3
Use the third equation of constant acceleration to calculate the height of the apex of the trajectory above the release height. Remember that the height of the trajectory depends on the vertical velocity, the acceleration due to gravity is approximately 9.81 m/s2, and the vertical velocity at the apex is zero.
Step 4
Calculate the total height to the apex of the trajectory.
Step 5
Calculate the time for the projectile to reach the ground from the apex of the trajectory. Because the projectile will land at a level lower than the release point, time for the projectile to reach the apex of the trajectory must be less than time for the projectile to reach the ground from the apex. The time down, tdown, can be calculated using the second equation of constant acceleration. In this equation, the displacement is negative because it measures the distance from the apex to the ground. In addition, the initial vertical velocity of the downward flight is zero.
Because time cannot be negative, each side of this equation must be multiplied by 1, resulting in the following:
Step 6
Calculate the total time the projectile is in the air by adding the time to reach the apex of the trajectory to the time to reach the ground from the apex.
Step 7
Calculate the range of the projectile. tdown= 1.10 s
The distance that the shot traveled under these conditions is 20.1 m. In our initial discussion of projectiles and the equations of constant acceleration, air resistance was considered to be negligible. The mathematics of air resistance are well beyond the scope of this book because they require solving differential equations. However, it may be of interest to know that if these initial conditions were used to solve this problem taking into account air resistance, a reduction of 1.46% in the range of the throw would be found. Considering air resistance, the throw would be 0.3 m less, or a total of 19.8 m.
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