City-Data Forum Uphill Running Equivalency Times (muscles, treadmills, arms, fast)
 User Name Remember Me Password [Register]
Please register to participate in our discussions with 2 million other members - it's free and quick! Some forums can only be seen by registered members. After you create your account, you'll be able to customize options and access all our 15,000 new posts/day with fewer ads.

12-11-2011, 01:34 PM
 Location: Atlanta 606 posts, read 1,600,739 times Reputation: 448

I've been searching on the web for information on this, but aside from this one "Science Blogs" article, I haven't found much of use. So let's see what insight the City-Data forums can provide'th me. (My expectations are low! )

I'm trying to figure out how to calculate "equivalency times" for uphill running. What I mean by that is --- if I run at a 5 degree slope, what pace is that equivalent to on completely flat terrain (i.e. a 0 degree slope).

Basically, since I only do uphill running on treadmills, I'm trying to figure out what my 1-mile time would be on a flat slope. Because I find treadmill running to be a bit unnatural at speeds over 7.5 mph, I prefer to simply increase the incline and stay in a range of 6.7- 7.5 mph (i.e. 8 - 9 minute miles). But this leaves me unable to gauge what my "1 mile time" would be on a flatter surface.

I came up with a methodology for this, but I'm not sure if it's accurate. It uses caloric burn to calculate a hypothetical pace. Here's how it works:

(1) Calculate number of calories burnt running 1 mile on 0 degree slope
(2) Take that number and set out target times (5 minute, 6 minute, 7 minute, etc.)
(3) Calculate calories per minute for each target time
(4) Determine number of calories burnt running 1 mile on a 5 degree slope
(5) Divide that number by the calories per minute for the flat slope

For instance, if one burned 100 calories running one mile on a flat slope, that would be 20 calories per minute if you ran a 5 minute mile. If one were to then run another mile at a 5 degree slope and that used 140 calories, and one did that in 7 minutes (hence, 20 calories per minute) --- this would, in essence, be the same pace (if I'm correct about the methodology.) Of course, the 7-minute, 5-degree slope would be more like running 1.4 miles, but the pace would essentially be the same.

For the record, these numbers are unrealistic --- I use them simply to illustrate the concept.

If my methodology is correct, then I'm estimating that my 9 minute mile at a 6 degree slope, would be equivalent to a 7 minute mile at a flat slope [which at least sounds plausible]. And I'd have to increase to a 11 degree slope at a 9-minute mile pace in order to be at an equivalent of a 6-minute mile on a flat slope.

Maybe this is too advanced of a topic for C-D, but was curious if anyone has any insight on this.

Last edited by DiderotsGhost; 12-11-2011 at 01:47 PM..

12-11-2011, 02:32 PM
 Location: Old Bellevue, WA 18,782 posts, read 15,927,668 times Reputation: 7968
Just my opinion/guess but I think there is no equivalency. Just based on experience it seems like higher speed vs. higher incline work the leg muscles in different ways.

12-11-2011, 07:10 PM
 Location: Albuquerque, New Mexico 2,117 posts, read 5,061,530 times Reputation: 1531
You can't use caloric burn because it's in relation to an individuals body and how they use energy. It's not a constant. Also, running on a treadmill isn't an accurate way to gauge running on flat ground. There is much more math involved, I didn't feel like doing it so I did a quick google search and found this:

"The VO2 equation for running up a slope must be added to that of level ground VO2. Therefore, VO2 for running up a 2% grade at 300m/min = 63.5 + 10.8 = 74.3 ml/kg/min.

Now, for "even paced running" when running up a slope, the 2 VO2 equations must be equal:
let level running velocity = y and slope running velocity = z

(y x 0.2) + 3.5 = [(z x 0.2) + 3.5] + [z x grade x 1.8]

For a grade of 2% and a level ground running speed of 300m/min, the velocity when running up the hill must equal:

0.2y+3.5 = 0.2z+3.5+0.036z
0.2(300) = 0.236z
60 = 0.236z

z = 254.24 m/min

Therefore, to maintain "an even pace" when running up a 2% grade, you must slow down from 300 m/min (level ground) to a velocity of 254.24 m/min while running up the slope.

"

Might be too advanced a topic for you. My expectations for you are low as I don't believe you'll have any idea what any of this means. . . especially if you think you can calculate times based on calorie burn. Ha.

12-12-2011, 01:20 AM
 Location: Atlanta 606 posts, read 1,600,739 times Reputation: 448
Quote:
 Originally Posted by tommodonahue You can't use caloric burn because it's in relation to an individuals body and how they use energy. It's not a constant. Also, running on a treadmill isn't an accurate way to gauge running on flat ground. There is much more math involved, I didn't feel like doing it so I did a quick google search and found this: "The VO2 equation for running up a slope must be added to that of level ground VO2. Therefore, VO2 for running up a 2% grade at 300m/min = 63.5 + 10.8 = 74.3 ml/kg/min. Now, for "even paced running" when running up a slope, the 2 VO2 equations must be equal: let level running velocity = y and slope running velocity = z (y x 0.2) + 3.5 = [(z x 0.2) + 3.5] + [z x grade x 1.8] For a grade of 2% and a level ground running speed of 300m/min, the velocity when running up the hill must equal: 0.2y+3.5 = 0.2z+3.5+0.036z 0.2(300) = 0.236z 60 = 0.236z z = 254.24 m/min Therefore, to maintain "an even pace" when running up a 2% grade, you must slow down from 300 m/min (level ground) to a velocity of 254.24 m/min while running up the slope. Read more: Speed vs. Slope " Might be too advanced a topic for you. My expectations for you are low as I don't believe you'll have any idea what any of this means. . . especially if you think you can calculate times based on calorie burn. Ha.
Wow, that's a bit arrogant. Overcompensating for other shortcomings in your life, perhaps?

Thanks for the info, in any case.

And my most sincere apologies for trying to learn something new and useful; and not coming into the discussion with a PhD in Physics.

I'm not convinced your methodology is useful, since you are looking at pure physical properties, rather than the amount of energy it takes a human to achieve "equivalent pace." In your very first sentence, you seem to suggest that you don't understand my concept. How an individual uses energy IS PRECISELY THE POINT!

The amount of meters per minute doesn't really tell me anything about the amount of exertion needed.

12-12-2011, 02:18 AM
 Location: Atlanta 606 posts, read 1,600,739 times Reputation: 448
Quote:
 Originally Posted by wutitiz Just my opinion/guess but I think there is no equivalency. Just based on experience it seems like higher speed vs. higher incline work the leg muscles in different ways.
Very true.

I've thought about this, as well. One of the reasons I prefer uphill running is that I find that it forces me to get a more full-body workout, as I have to use my arms and upper body more, to power up a slope.

So any 'equivalency pace' would be flawed based on this. But I still find it a useful concept. Maybe there can be no true 'equivalency pace', but there is certainly a pace at which one exerts an almost identical amount of energy, even if the two styles of running may work different muscle groups.

12-12-2011, 03:19 AM
 Location: Albuquerque, New Mexico 2,117 posts, read 5,061,530 times Reputation: 1531
Quote:
 Originally Posted by DiderotsGhost (My expectations are low! ) Maybe this is too advanced of a topic for C-D, but was curious if anyone has any insight on this.
You didn't seem to keep the arrogance to a minimum, so neither did I.

Also, not only is energy calculated, but also mechanics, oxygen, so on and so fourth. You're an idiot if you think you can calculate this based on 'caloric burn'. Especially considering you have absolutely no way to calculate that.

Quote:
 Originally Posted by DiderotsGhost Overcompensating for other shortcomings in your life, perhaps?
No, not at all. I'm completely happy with my life and what I've accomplished. Which, for me, allows me to be confident in being a complete dick to you over the internet. Please tell me, based on your over generalized and fact ess statement, what shortcomings I may have in life. Please, let me know.

12-12-2011, 07:38 AM
 Location: SoCal - Sherman Oaks & Woodland Hills 12,975 posts, read 31,845,442 times Reputation: 10491
Quote:
 Originally Posted by DiderotsGhost Wow, that's a bit arrogant. Overcompensating for other shortcomings in your life, perhaps?
How rude!! He gave you great info and you respond with this?

I'll make my answer very very very simple for you - either run flat on your treadmill, or go out and run on a flat road, measure your results then compare to the uphill treadmill.

Tommodonohue, GREAT POST in post #3!!!

12-12-2011, 10:55 AM
 Location: SE Michigan 968 posts, read 2,433,785 times Reputation: 499
why do we need a physics lesson? Running outdoors vs running on a treadmill are comaring oranges to apples.

Pick a hill and go like hell up it. The hill always wins. Don't worry about the numbers and just run.

12-12-2011, 12:09 PM
 Location: A coal patch in Northern Appalachia 7,492 posts, read 8,129,414 times Reputation: 9269
Do you really think you get a "full-body workout" by running up hill. That's like the people who walk with the little handweights and think they are getting an upper body workout.

12-12-2011, 12:43 PM
 Location: SE Michigan 968 posts, read 2,433,785 times Reputation: 499
Quote:
 Originally Posted by villageidiot1 Do you really think you get a "full-body workout" by running up hill. That's like the people who walk with the little handweights and think they are getting an upper body workout.
nothing like walking with hand weights.

Go do it. Sprint as fast as you can up a hill.

Its not a strength workout per say. Its a measure of cardiovascular fitness and endurance. Again we need to compare apples to apples.
 Please register to post and access all features of our very popular forum. It is free and quick. Over \$68,000 in prizes has already been given out to active posters on our forum. Additional giveaways are planned. Detailed information about all U.S. cities, counties, and zip codes on our site: City-data.com.