Physics of Climbing vs. Walking (Horizontal)

[WWGD]

Hi, please forgive my ignorance here; I barely have just a basic undergrad. training in physics:

I was trying to see if we can use physics to determine how much harder it is (say, by amount
of energy/calories spent; maybe someone can suggest a better measure? ) to climb stairs,
given the slope of the stairs, than it is to move the same distance horizontally, i.e., let's
model a right-angle triangle with sides a,b and hypotenuse c , so that c^2=a^2+b^2.
Say we have a constant slope θ. Can we use physics to determine how much harder is it to go along the length c of the hypotenuse than it is to move( by walking, of course) the same c units horizontally? Of course, we're oversimplifying in assuming the movement up the stairs is done
along a line; maybe there is a better way of modeling this?
Thanks.

 

[HallsofIvy]

One way to do that is to calculate the increase in potential energy by that increased height. That increased energy must be equal to the work done in climbing.

 

[sophiecentaur]

This sort of problem is easier to solve when you are talking about mechanical devices with motors and wheels and even then, there are issues of getting the best efficiency by doing work at the optimum rate. The best you can do, initially, is to base calculations on the height achieved (Gravitational Potential Energy) but including the human body makes it much harder. Merely walking along on the horizontal, takes Power. You then need to add the height gained.

If you have done any running or cycling, you will have noticed what a difference any small up or downhill slope makes to the ease of moving. I am very skeptical of the use of pedometers to estimate the energy use at work. There must be a huge number of variables in evolved. A common method is based on measuringe the gases in your exhaled breath.