The intersting thing about walking up stairs is that no matter how tall you, you will take the same number of steps to get up the stairs, assuming you don’t skip any steps.
The taller person is likely heavier and will take just as many steps as the shorter person, but being taller also means your legs are longer so you won’t have to lift your knees as high for each step.
Stair steps are typically 7 to 7 3/4 inches high.(17.78cm to 19.68cm) . A person that is 5 foot tall will have to lift his or her knee much higher relative to their body than a person 6 foot tall.
So assuming that both people have the same BMI and leg to body ratio, who would get more fatigued?
The simple answer here is that the amount of energy you expend to walk up stairs is proportional to mass, with height making no contribution. But the mass of each leg (which could be related to height) would be a factor.
Asking “Who gets more fatigued” complicates the matter to the point where a direct answer may not be possible. You must, for example, consider the physical condition of your subject person? An elite athlete could run up many steps with no sign of fatigue, while someone with lung cancer might collapse after 2 steps. Steps that are abnormally large might disadvantage an abnormally short person.
Wouldn’t lifting your leg higher burn more energy? Your leg has mass and you need to use energy to raise it. So someone who has shorter legs has to use a wider range of motion to achieve the same step.
In walking it seems that energy per stride was pretty linear with mass, but that taller people had longer strides and burnt less energy.
It also appears that in stair climbing, two steps per stride burnt less energy. http://blogs.discovermagazine.com/seriouslyscience/2014/10/06/taking-steps-one-time-two-burns-calories/
I am 6’2" and when I graduated High School I was 145lbs which is way less than the average, yet I always climb two or more steps per stride on stairs because it is uncomfortable to only use one step. Compared to a heavier individual, or an individual that was more likely to use individual steps I would expend less energy.
Unfortunately I was unable to locate good statistics for height relating to height and 2 steps or 1 step per stride.
Today the average American man over age 20 weighs ~195.7 pounds which is pretty close to my weight, and I am now well past 40. So compared to the average American man the difference would mostly depend on average steps per stride but would be very similar to a shorter individual who tended to average the same number of steps per stride.
You do more than just lift your leg higher. Your muscles lift your body weight with different leverage, depending on the angle of the knee when delivering the force to lift your body. Analogous to lifting a weight in your hand, with your elbow bent at different angles.
I am assuming that the rise of a standard architectural step maximized the efficienty of a person of average height, and the cost rises as your height deviates from that standard. A person 4’10" would pay a penalty the same as a person 6’10".
It would be interesting to know if stairs are designed with different rise in, say, Denmark and Ecuador.
I would imagine that the rise variation in the USA stems from the fact that the distance of the rise has to be a factor of the total height of the stairway. You could not have every step exactly 8 inches if the total rise needs to be 165 inches – there would be five inches left over.
THE MAXIMUM RISE AND MINIMUM GOING OF STAIRS - “Going” is effectively the tread depth but takes account of the ‘nose’ which is the overhang at the front.
Private Staircase (Domestic) Max Rise = 220mm, min going 220mm. (220mm = 8.66")
Utility (Public) Max Rise = 190mm, min going 250mm.
General Access (Semi-Public) Max Rise =170mm, min going 250mm.
Pitch (steepness) is also important.
The maximum pitch of stairs
Private Staircase(Domestic) = 42° Maximum.
Utility (Public) = 33° Maximum.
General Access (Semi Public) = 38° Maximum.
Please Note - that your stair tread cannot be too long or the riser too short because building regulations also state: Twice the rise plus the going (2R+G) should be between 550mm and 700mm.
I think this topic requires too much-advanced physics and math even though it seemed simple at first.