Knee Forward/Hip Straighten Force (Compound)
Based on an adult of 70kg, we know the combined weight of the upper leg, the lower leg & the foot is approximately 11.55kg, so from the hips down, both legs add up to 23.1kg.
Performing a One Rep Max (1RM) on a leg press machine, the average person should be able to leg press 1.8 to 2.2 times their own body weight. So if an average person weighs 70kg, they should be able to 1RM leg press anywhere between 126kg & 154kg Anywhere below this is below average performance, and conversely anywhere over being above average.
It is interesting to note, using the leg press machine a person will be able to press more weight than if they were to perform the similar, but different weighted Squat exercise, because the squat introduces additional stresses to the back & shoulder areas.
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What can we tell from this then?.. We are able to tell the minimum 'body-weight' only requirements on this DOF, and also the 'maximum-weight' (incl 'body-weight') this DOF is capable of moving.
PER LEG (EACH) KG/N
Body-Weight Only: 11.55kg/113N
Max Capable Weight: 74.5kg/735N
(Centre of average group)
Area Total-Length Weight COM
Head: 23cm 4.97kg 15cm
Torso: 51cm 33.81kg 34cm
UpArm: 29cm 2.31kg 14.5cm
LowArm: 27cm 1.33kg 13.5cm
Hand: 18cm 0.42kg 9cm
UpLeg: 39cm 7.35kg 26cm
LowLeg: 42cm 3.15kg 21cm
Foot: 7cm 1.05kg 3.5cm
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Before we proceed to calculate the torque necessary to perform this exercise it is important to remember this is dissimilar to all past examples in that it's the first compound movement, employing many muscle groups. This type of movement is also what's categorised as an 'explosive exercise' in the sense that it is a high force, low speed movement. It is also worth noting in the starting position the person is in an almost fetal position, using their strength to 'explode' into a straightened-legged position. This exercise requires the application of torque about the hip & knee joints for the most part. It's important to note that the most demanding stages when performing a weighted leg press is when the legs are moving away from/as they're approaching the 45degree starting position.
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Calculating 'Explosive' Torque
Before we look at the weighted exercise & because the distribution/contributions of the hip torque & knee torque for this move is somewhat of an unknown, we will first explore what forces might be acting on these joints whilst performing this move unweighted (only moving the leg mass) to gain a greater understanding of how the forces are interacting with one another. When calculating our torque values, it is important to remember the movement we our performing is essentially just stretching the legs out straight (insofar, we're not turning the leg around in a large arc/circle), the reason this is important is because we need to remember these values are essentially a 'sliding-scale' of 'holding torques' to produce a fluid movement.
Hip Torques
•In the starting position, the upper leg is pointed vertically up, and because our thigh is only around 15cm deep (skin in front to skin on back of leg), our upper leg has a COM (7.35kg) balanced centrally over the hip so in this starting position our upper legs mass of 7.35kg is acting directly over/on the hip joint.
•The hips 7.35kg COM centred directly over the hip in the starting position will slowly extend forward during the movement to a fully extended 13cm from the hip joint. Just briefly/momentarily before reaching the 'fully extended' (legs straight) completion of the movement is when the most torque will be acting on the hip joint at 13cm away.
•So the least hip torque (from upper leg) will be in the starting position, reaching maximum torque 13cm away, so a torque range of 0-95kgcm.
•The mass of the lower leg (3.15kg) is also acting on the hip joint during the starting position. Just briefly/momentarily before reaching the 'fully extended' (straight legged) completion of the movement is when the max torque will be acting on the hip joint at 60cm away. So the least hip torque (from lower leg) will be in the starting position, reaching maximum torque 13cm away, So a torque range of 0-189kgcm.
•The mass of the foot (1.05kg) is also acting on the hip joint during the starting position. Just briefly/momentarily before reaching the 'fully extended' (legs straight) completion of the movement is when the most torque will be acting on the hip joint at 84.5cm away.
So the least hip torque (from foot) will be in the starting position, reaching maximum torque 84.5cm away, So a torque range of 0-89kgcm.
•If we add the foot, lower leg & upper leg max torques on the hip (per side/hip) is looks like this,..
Stage of Exercise Torque
Starting Position 0
Mid Range 186kgcm/18Nm
End Position (Max) 373kgcm/37Nm
Knee Torques
•The lower legs (3.15kg) COM is at a fixed distance of 21cm from the knee.
•The foots (1.05kg) COM is at a fixed distance of 45.5cm from the knee.
•So the lower legs 3.15kg x 21cm is 66kgcm, & the foots 1.05kg x 45.5cm is 48kgcm. So there is collectively 114kgcm (11Nm) of torque acting at the knee joint.
So the torque acting at the knee is a constant of 114kgcm, or 11Nm.
This goes some ways to understanding the basic dynamics of this exercise/movement. We now know doing this movement 'unweighted' puts;
•A Variable torque of between 0-37Nm on the hip.
•A Constant torque of 11Nm on the Knee.
Over three times as much torque at the hip compared to the knee.
Exploring weighted Leg Press
In both illustrations of the Leg Press machine at the beginning, we can see that the added weight is fixed on top of the platform on which it rests, that is to say it is not sat on a platform which is attached to a pivot acting as a lever. Because of this and to simplify the conclusion of this investigation we shall assume that because the weight runs parallel to the legs, behaving as though it's COM is zero in relation to our legs, that it's effect on our 170cm/70kg person is simply amplifying the forces required to move his legs 'unweighted'.
In our weighted example, we will assume the person is on the low end of the average persons performance group & can leg press 1.8x times their own body-weight at 126kg on the machine. As usual, we will treat this weight with a 'Per Leg/Per Body Side' approach, so the weight each leg needs to press is 63kg.
We should also recall our unweighted movement and the hip & knee torque requirements of that. We will look at the total torque output and translate our hip & knee into a percentage of this.
DOF MAX TORQUE PERCENTAGE
Hip 37Nm 77%
Knee 11Nm 23%
Output 48Nm 100%
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To move a weight of 63kg a distance of 40cm up a 45degree incline with zero friction;
Weight: 618N/63kg
Force: 437N/44kg
Distance: 40cm
Total Torque Requirement: 175Nm
Dividing this 175Nm Total Torque Requirement across the hip & knee joints;
Hip: 135Nm
Knee: 40Nm
Now adding our body weight only torque requirements looks like,..
DOF 63kg Only B/W Only Total
Hip 135Nm 37Nm 172Nm
Knee 40Nm 11Nm 51Nm
Total Output 175Nm 48Nm 223Nm
Summary,
Unweighted Leg Press;
Hip Torque (MAX): 37Nm
Knee Torque (MAX): 11Nm
Weighted (63kg) Leg Press;
Hip Torque (MAX): 172Nm
Knee Torque (MAX): 51Nm
