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*

*where*

- 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?

Nitin Jain,

ReplyDeleteVery well written and nice calculation too....i feel climbing/running the stairs is more of a hill climbing, pace is going to be lot different compared to what you have calculated.....after some time it becomes really steep and find it quite tough to maintain the pace.....i would say pace would be similar to 4 to 6% gradient running route and what pace is ones pace for that stretch would more nearest calculation....and one more reason why pace drops after certain time is legs becomes very stiff because of the gradient....feel would be around 200 to 250 steps per minute based on ones fitness and how long one is going to do it also will have a impact on it.

Thanks Anil for comment.

ReplyDeleteI agree there are obvious flaws. I couldn't find much information on this. So, I ended up doing some crude calculation.

As I said, I expect this calculation to work for same time frame as running. So, if somebody can run, 1 km in 4 minutes, I will expect him climb 490 (+15%) stairs in four minutes. Let us assume, same person may be able to do 400 metres in 60 seconds (pace of 2:30), I will expect him to do approximately 200 steps (+15%) in one minute.

I am hoping to validate this calculation when we result from skyscrapers. My current guess is that very good amateur runners should be doing around 165 steps per minute at event. Hoping best timing to be roughly 5 min 15 seconds.

Nitin,

ReplyDeleteI agree with you, it makes sense...as you said june 15th will give more clarity too. you mean to say it is 850 steps at 490/200 steps per minute will be done in 2 to 4 minutes....that is quite fast i would say.....no comparison to it....just a post from my FB today ironically.... https://www.facebook.com/anil.kadsur i am not building too much pace, am looking at endurance rather.

I meant 850 steps at 490 / 165 steps per minutes. It should be done in around 5:15 minutes.

ReplyDeleteI saw your post. Very inspiring. I tried doing little reverse engineering on that. I see that you did 3275 steps up and 3231 steps down. Let me assume (and please correct if I am way too wrong) that you spent 2/3 time in climbing up. So, You climbed 3275 steps in 40 minutes. That makes approximately 82 steps per minutes. Putting this reversely in my formula, your running pace should be (490 / 82) min per km = 5.976 mins per km. Is pace anywhere close for your run of 1 hour? I say 1 hour because you are still working out for one hour out of which you spent 40 minutes steps climbing.

Also, initially legs muscles may not be tuned for steps climbing as it may be for running (or cycling). But once you are equally good in both running and step climbing, I will expect this formula to converge. I hope I am making some sense in my discussion. :)

A little mistake in above comment. I meant 850 steps at 165 steps per min. 165 step is calculated using '490' / '3 mins per km'

ReplyDeleteI think the best time will be under 5.15. Gathering what I read online the best time for the CN Tower climb which is a total of 1776 steps was 8. something in 2013. As incredible as it sounds I believe there should be elite athletes who should be able to climb 850 steps in less than 5 maybe even sub 4.30.

ReplyDelete@Rupak I am sure elite athletes will do sub 4:30. I was just thinking of guys and girls who are little better than me. :)

ReplyDelete