The Physics of Exercise – Climbing (stairs)

Second installment – an easy one: what about climbing (or, for most of us, climbing stairs)?

Climbing (Stairs)

The only energy relevant here is that of raising your own body (please note that I dont account for the energy expended holding yourself against the wall, even though I’d assume this might be substantial. This is all part of the inefficiency factor…)

  • Bodyweight 100kg
  • Height climbed: 150m (50 floors@3m/floor; 600steps@25cm/step))
  • Movement of body: energy = 100[kg] x 150[m] x 10 = 150,000J = 150kJ = 36kcal
  • Total energy for one floor / one meter / one step = 3000J/1000J/250J

Again using an inefficiency multiplier of 3 this leads to

  • Total energy expended =36kcal x 3 = 108kcal
  • Carb or protein equivalent = 108[kcal] / 4 = 27g
  • Fat equivalent = 108[kcal] / 9 = 12g

So to summarise: the work (in the physical sense) that I would need to do to climb 150m is 36kcal. In order to achieve this, my body would need to expend 108kcal of energy, which is the equivalent of 27g of carbs (or 12g of fat).

Appendix – Fundamental Relationships

  • Earth acceleration ca 10 m/s^2
  • Energy of lifting 1kg by 1m = 10J
  • 1kcal = 4.19 kJoule
  • 1kcal = 4g carbs = 4g protein = 9g fat

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