Friday, May 2, 2014

Staircase Climbing Pace- A Runner’s Guide

When I decided to participate in India’s first stair climbing race- Skyscrapper dash, first question that hit me was, how much time will take for me to run those 850 stairs. (This is what a calculative runner becomes over time.) 850 stairs sounded a lot. I have never participated in stair climbing race. I have no idea if I should run on stairs or just walk with faster pace. What I needed was some correlation between my running pace and stair climbing pace.

After working out (mathematically), I came up with this formula:

Number of Steps per minute ≈ 490 / running pace in mins per km. 

Note: This formula is applicable for similar time frame. So, if you are expecting your staircase race to last for 10 minutes, use your running pace that you can maintain for 10 minutes. Also, ensure to convert your running pace from mm:ss to xx.yy. So, lets say if you are running pace is 4:40 mins per km, you should use 4.67 mins per km in above formula. 

So, here is the workout:

Energy required for climbing stairs:

Energy in kcal = (m * g * h) /(eff * (joules per kcal))                               
                                    = m * 9.81 * 0.16 * number of steps per min /( 18% * 4184)

  • m = mass of person climbing stairs
  • g = acceleration due to gravity
  • h = height = 0.16 (height per step) * number of steps per min
  • eff = efficiency of human legs = 18 - 26%. Assuming 18% for calculation
  • joules per kcal is used to convert joules in kcal. Remember food calorie is actually 1 thermodynamic kcal. 

Approximate formula for calculating energy spent while running:

Energy in kcal = 1.02 * m * d 
Energy in kcal per minute = 1.02 * m * d / t                   
                                    = 1.02* m / pace


  • m = mass of person in kg
  • d = running distance in km
  • t = time taken in minutes
  • pace = d/t in minutes per km

Assuming that a person will be able to generate same power (spend same energy) in both activities,

(m* 9.81* 0.16* number of steps per min * 100) / (4184* 18) = 1.02* m / pace
=> number of steps per min = (1.02* 4184* 18) / (9.81* 0.16* 100) / pace                   

 490 / pace                      

Oh yeah, I know this is oversimplified and there are obvious flaws in this. Following are limitation of this formula that I can think of
  • A person can spend more energy while staircase climbing compared to running in same amount of time.  Thus equating energy spent in running and staircase climbing may be wrong. I will expect a person able to climb 10-15% more stairs as predicted from above formula. 
  • This formula uses muscle efficiency for calculation of energy spent while staircase climbing but not while running. This will vary from person to person (and probably with activity and time). This will introduce error in formula.
  • Formula to calculate energy while running is just an approximate (but so is calculating number of steps. :) )
  • Using correct pace is pretty important. A slight variation in pace can introduce huge error. If a person is just going to do stair climbing for 5 minutes but uses pace for his 5 km race, do expect an error there. :)

Do let me know if you think of other possible errors in this formula.

If somebody verifies this, please let me know, how close were you?