Tuesday, February 26, 2019

A realistic magnitude for the extreme human pushing force

Following Simon's latest post On the classic crushing trap i wondered why on earth the sliding block in the false entrance to the Tomb of Horrors was made so big. With a mass of 170 tonnes, it weighs 17 times as much as the biggest blocks used in the pyramids.

To keep characters locked inside until they starve to death, this certainly seem overkill (at least if you are forced to figure out how the hell this gigantic this moves seemingly on its own) But how how strong can we actually assume that characters in D&D are? Would they, given enough men, be able to push it?

The AD&D DMG explains that a character will be able to lift the equivalent of this own body weight over his head with a strength score of 18. For each percentage point of exceptional strength above 18, he will be able to lift more up until the limit of around 500 lbs (230 kg) if the character were to weigh 210 lbs. This is actually pretty spot compared to the real world as the current record according to Guinness is at 233 kg. (or 2,3 kN).

The AD&D DMG, however, produces no numbers that i can find of how much weight a character might push. So what kind of pushing force can a human being actually produce? We can start by looking at real world weight lifting records to get an impression of how much force the muscles in a human body is capable of. If we assume ideal conditions we should start by looking at bench press records for arm pushing strength and leg press records for leg pushing strength. These are 488 kg (1075 lbs) and 1118 kg (2465 lbs) respectively, giving a 1606 kg total. or 15,7 kN. This number would certainly be an extreme upper limit of the human muscles considering that no reducing factors are considered and the muscles are seen at their individual limits.

In engineering we often use the terms of upper and lower bound solution meaning that the real solution must be in between these two, so looking at the before mentioned records of actual weight lifting where the contestant also has to balance whatever he or she is lifting we are looking at only 15% of the extreme solution. It can therefore be concluded that the actual maximum pushing force of the human body lies between 2,3 kN and 15,7 kN.

The factors that determine where the actual maximum lies would be balance, footing, inclination and the strength of human bones. First, even though pushing an object is not the same as lifting something over your head, there is still some sort of balance that must be kept. Second, the limit is also strictly subject to the footing since you would slip or slide when the limit of the friction force between the floor and the soles were met by the pushing force. This factor can be mitigated by pushing something vertically over your head, but then balance becomes more of an issue. Third, unless you are pushing something directly over your head, not all of the force you create will be translated horizontally. The force will also have a vertical component. Last, The maximum forces found above was found by simply adding the maximum force of the muscles in the legs and arms together. I have seen videos of men breaking their own bones from the force of their arms alone, so it seems very plausible that the combined force of two muscle groups could break bones before reaching their extreme.

So in the end, there are too many factors to make a more precise presumption than a feeling that going over 50% of the upper bound solution would seem too unrealistic as there are many factors that will always apply. So even though this can only serve as a figure of magnitude of the maximum pushing strength of the human body, A force of 8 kN shouldn't be too unrealistic.

3 comments:

  1. 50% seems a good benchmark to allow a ability check, to see if the character can take advantage of his circumstances and eke out success. Thus, if my overhead lift is 100lbs (~45kb), my upper limit (for pushing) should be 666.667lbs (or ~303.03kg) and my 50% should be 333.33lbs ~ meaning I can reliably push 333lbs but if I try to push more than that, I need to make a Strength check (and I shouldn't be able to push more than 666lbs).

    Assuming I'm following your logic, that is . . .

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    1. That idea is so great! I never thought about relating the ability check directly to the real world factors influencing an action or even using this as the rules not provided by the DMG. It even fits perfectly to be able to modify the roll based on the listed factors. My goal was to find a simple number that could be used as an estimate, but the upper and lower bound is even better to have as it provides room for those factors modeled by the dice.

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