Bodyweight Need A Pushup Math Maven

[Mirek]

Rough estimate would be: 0.7 * bw * ( 1 - (e/sqrt(b**2 - h**2))),

where
bw - bodyweight
e - total elevation (from ground to hand)
b - shoulder height
h - arm length

It is based on the assumption that on ground you support 70 % of your bodyweight.
It also probably does not have a proper asymptotic behaviour (e.g. when e = b), so it's really rough.

 

[pet']

Hello,

@Mirek
Thanks for the maths! I'll measure my arm this evening then to get a figure.

height and length are in meters ? centimeters ?

Kind regards,

Pet'

 

[Mirek]

@pet' should not matter as long as you are consistent, e.g. all lengths in cm

 

[Ian V]

This is a link to an article which shows the % of body weight lifted in various positions..

Kinetic Analysis of the Push-Up: Which Version Is Hardest?

 

[damogari]

Out of curiosity I tested my push ups on weight scale - used both hands, diamond push up.

Bodyweight: ~104kg

With feet on the ground
- top position ~72kg (69%)
- bottom position ~78kg (75%)

With feet elevated 20cm
- top position ~74kg (71%)
- bottom position ~79kg (76%)

With feet elevated 40cm
- top position ~76kg (73%)
- bottom position ~81kg (78%)

So the assumption that we are pushing about 70% of bodyweight is pretty accurate

 

[mprevost]

According to this study:
Kinetic Analysis of Several Variations of Push-Ups

Ebben, William P1; Wurm, Bradley2; VanderZanden, Tyler L2; Spadavecchia, Mark L2; Durocher, John J2; Bickham, Curtis T1; Petushek, Erich J4

Journal of Strength & Conditioning Research:
October 2011 - Volume 25 - Issue 10 - pp 2891-2894

The relationship is as follows. I have plotted upper body elevation and lower body elevation and resulting % bodyweight loading. I have also calculated the regression equations based on their data so that you can calculate the % bodyweight for your own elevation.




The regression equations are on the graphs. Y=%bodyweight. X = the elevation you are using. Note there are different equations for upper body and lower body elevation. There are only 3 data points to work with but they look plenty linear and the R2 value is good.

 

[Mirek]

After adjusting for the bodyweight supported on the ground (less than 70%) it is pretty close to
the above formula, which was derived only for the upper body elevation.

 

[Steve Freides]

Since I started this thread, I'll post an update. I'm still working on my 1APU, currently taking an Easy Strength approach, and am using 1 arm and both legs at a 12" elevation. I am "stuck" here but not in a bad way - this seems to be a place where I can get away with less than good form but it's easy enough that I can also tighten up my form and better address my weaknesses. My plan is to hang out here for a while - I can currently do a few doubles and triples, and I'd like to be able to do 5's in good form for a few sets before I move on. My main mission is to get stronger enough at these that the CNS component is less taxing and I can do more volume. I may even go back to a higher elevation to get in some more volume.

-S-

 

[305pelusa]

@mprevost : Really awesome post! That's the kind of analysis we need more of in training! If I may suggest a couple of things.

Note there are different equations for upper body and lower body elevation.

There's no reason why you'd need two different plots for this data. Feet elevation can simply be thought of a "negative" height. This will allow you to have 5 points in one graph.

There are only 3 data points to work with but they look plenty linear and the R2 value is good.

They don't seem very linear to me. Note how the intercept is rather off. An R^2 value of .984 in a graph of only 3 points is really low. This is experimental data done in a pretty good study. We'd want an R^2 value of almost 1 with whatever regression we use.

Fundamentally, this makes some sense because hand elevation plays with angle, which is ultimately a sinusoidal issue. So a linear regression might not work as well.

If you feel like it, try it again with all 5 points and regress it with a cubic function. You'll be able to get an R^2 value of virtually 1.




Fun thread. Big fan!

 

[mprevost]

Wow, great, thanks. That was nicely done. I am a physiologist not a math guy so anything beyond a simple regression baffles me. Thanks for doing that. The equation could be very useful.

 

[mprevost]

Next step is to create a simple chart with inches of elevation (or - elevation) and % bodyweight

 

[pet']

Hello,

So, when I do a OAOL PU, with my foot on a 10 inches support, with a bdw of 61 kg, I press 61 * 62% = 37 (rounded). Is that correct ?

Kind regards,

Pet'

 

[305pelusa]

Hello,

So, when I do a OAOL PU, with my foot on a 10 inches support, with a bdw of 61 kg, I press 61 * 62% = 37 (rounded). Is that correct ?

Kind regards,

Pet'

You measured that or calculated it using a formula?

 

[pet']

Hello,

@305pelusa
I looked at the graph.

Kind regards,

Pet'

 

[305pelusa]

10 inches = 25 cm. Your foot is the one raised, so that's negative 25 cm. That corresponds to roughly 66-67 % of your Bodyweight from the graph I posted.
You can see @mprevost graph gives essentially the same value. It's all rough calculations so me being so picky about the regression and multiple points isn't that helpful anyways hehe.

Using the formula is the most exact but eye balling the graph is good enough.

 

[pet']

Hello,

@305pelusa
I just wanted to get a ballpark idea of this kind of press. This is quite frustrating because I still can not press the 32 hehe.

Thank you very much for your help

Kind regards,

Pet'

 

[305pelusa]

Hello,

@305pelusa
I just wanted to get a ballpark idea of this kind of press. This is quite frustrating because I still can not press the 32 hehe.

Thank you very much for your help

Kind regards,

Pet'

Let's do a bit of math.
Your weight is roughly 60 Kgs. So your OAPU with feet raised is pushing roughly two thirds of that (40 Kgs).

The ratio between horizontal and vertical press for most people seems to be around 1.5 to 1. So divide your horizontal press of 40 Kgs by 1.5 (so 26 Kgs).

If I had to guess, you're capable of Presses with 26 Kgs for a few reps (since you can rep out the OAPU) and maybe capable of a couple of singles with 28 Kgs. Is this correct? The 32 Kgs one still seems a little heavy. Maybe a bit more to go hehe

 

[pet']

Hello,

@305pelusa
You are quite precise ! My current 1RM for the press is 30kg For the 28, 3 in a row for both sides

I have a bit more to go for the 32 yes ! I am on my way hehe!

Kind regards,

Pet'