Push Up Strength

So this is a follow-up to my single leg strength post. It is probably going to be a rather quick read. In this installment, I am going to offer a taxonomy of push up variations that can be implemented during a home workout. Let me preface this article by saying that this is not by any means going to be an exhaustive list, as there are countless push up variations that all come with their unique benefits. Instead, I will select only a couple of exercises and focus on the strength demands on the upper body.

One of the most straightforward ways of controlling intensity is elevating the feet, to make the exercise harder, or the hands, to make it easier. According to Verkhoshansky (2003), roughly 65% BW are on the hands in a regular pushup. Elevating the feet by 30.5cm increases this amount to ~72%. An even bigger elevation of 61cm results in ~74% BW being put on the hand. Intermediate values can be approximated via linear interpolation. The load on each hand is then obtained by simply dividing the total load by two.

Analogously, elevating the feet decreases the load on the hands. Interestingly, the jumps in intensity are significantly larger in this case. While the relative difference in intensity between a 30cm and 61cm elevation of the feet is a mere 2%, it is as much as 35% (24% vs 58%) when the hands are elevated.

Training loads resulting from different inclination angles are presented in the following Tables. The first table lists the training load of incline push up variations with hand elevations from 92 to 0 cm. The second table lists the respective training loads for decline push ups. As mentioned above, the difference between distinct height in the incline push up yields much more meaningful changes in the training load than the same changes in the decline push up.

Height	Bodyweight	Both Arms	One Arm
92	24.00%	19.2	9.6
86	27.00%	21.6	10.8
80	31.00%	24.8	12.4
73	34.00%	27.2	13.6
67	38.00%	30.4	15.2
61	41.00%	32.8	16.4
54	45.00%	36	18
46	50.00%	40	20
39	54.00%	43.2	21.6
31	58.00%	46.4	23.2
26	60.00%	48	24
21	61.00%	48.8	24.4
16	63.00%	50.4	25.2
10	64.00%	51.2	25.6
5	66.00%	52.8	26.4
0	67.00%	53.6	26.8

Height	Bodyweight	Both Arms	One Arm
0	67.00%	53.6	26.8
5	68.00%	54.4	27.2
10	69.00%	55.2	27.6
16	70.00%	56	28
21	70.00%	56	28
26	71.00%	56.8	28.4
31	72.00%	57.6	28.8
39	73.00%	58.4	29.2
46	73.00%	58.4	29.2
54	74.00%	59.2	29.6
61	74.00%	59.2	29.6
67	74.00%	59.2	29.6
73	74.00%	59.2	29.6
80	75.00%	60	30
86	75.00%	60	30
92	75.00%	60	30

Another way to make push ups harder is to switch to single arm variations. For the sake of simplicity, I am going to assume that load distribution between the arms and legs remains constant regardless of whether a bilateral or unilateral push up is considered. This might be a gross oversimplification, though, so take it with a grain of salt. In my super simple model, the load per hand then simply corresponds to the total load.

The following Figure ranks pushup variations according to their relative intensity. Each bar in the chart represents the training load that is placed on one arm. Interestingly, even the easiest single arm variation, with a 60cm hand elevation, is harder than the decline pushup with a 60cm elevation of the feet. This again points to a problem with calisthenics-type exercises: difficult scalability. Assuming a bodyweight of 80kg, a 60cm elevation of the feet yields a total load of around 47Kg, which translates to 23.5Kg for one arm. In contrast, a single arm push up with a 60cm hand elevation will result in a training load of approximately 33Kg for the working arm. That is a 29% difference in training loads. Putting those values into the Epley 1RM equation indicates that an athlete needs to be able to perform 12, 60cm decline push ups before doing a single 60cm incline push up. This does not take into account the increased complexity of the latter that comes from the stability demands in the transverse plane.

Of course, strategies such as double- and triple progression can be implemented in order to attenuate this issue. A daily undulating program can easily be implemented by choosing the hardest exercise one can do (potentially for a single rep) for a strength day, the next hardest (where something like 6-20 reps can be performed) for a hypertrophy day and finally, the next easiest variation for a strength endurance day. So, with a rudimentary knowledge pf program design, the challenges that come from scalability can be overcome, at least to a certain degree.

Also, the set of push ups I evaluated for the sake of this article is rather small. Additional variations, such as sliding single arm push ups and archer push ups can be used as intermediate steps when progressing from bilateral to unilateral training. There’s always the issue of standardization, though. As I mentioned in my single leg article, it is hard to quantify the amount of help provided by the assisting limb in real time. Subjective measures such as RPE or RIR are probably one’s best bet in this case.

Again, this article does not aim at scientific accuracy or even correctness. Rather, the goal was to provide a conceptual, easy-to-implement framework for an easier control of training variables during the lockdown.

I’ll probably do something on pulling exercises in the near future as well, so stay tuned. So long,

don’t get hurt

Reference:

Duffey, M. J., and V. Zatsiorsky. „Load supported by the upper extremities during incline and decline pushups.“ Medicine & Science in Sports & Exercise 35.5 (2003): S62.