# B How much time it takes to walk a certain distance?

1. Apr 1, 2017

### george95

Hello,
I have one issue: I would like to know how much time will it take a pedestrian to walk certain distance (based on its movement speed), but taken into account the slope that his walking path takes?

I checked a number of sources and most of them quote the speed of an adult, healthy, pedestrian (I assume an average of male and female values) to be:
1.4 meters/second. Which is 84 meters/minute or around 275 feet/minute.

However, can it be that this 1.4m/s is actually the value in case the pedestrian is walking on a relatively flat terrain? What happens he is walking on a sloped terrain, of a certain angle!!
For example, a pedestrian is walking on a terrain which has a constant slope angle of 20 degrees. How does those 20 degrees reduce the 1.4 meters/second walking speed?

I would be grateful for any kind of reply.

2. Apr 1, 2017

### rootone

If the person is walking uphill they will have to expend additional energy (because of working against gravity).
So assuming they don't deliberately speed up to compensate, but keep walking at a comfortable rate,, that rate will be slower than on flat ground.
Conversely they need less energy to travel downhill, so they will move faster without any additional effort, in that case gravity is assisting them.

3. Apr 1, 2017

### george95

Thank you for the quick reply rootone!
Yes, but how much slower in relation to the angle of the slope?

4. Apr 1, 2017

### rumborak

That will probably be very hard data to come by. This isn't a question that can be answered with a convenient formula, it has to be established empirically.

5. Apr 1, 2017

### george95

Thank you for the reply rumborak.
I would accept empirically derived formulas as well!

6. Apr 1, 2017

### rumborak

What you *might* be able to do, with a bit of handwaving, is to say "on flat ground a person burns so many calories, i.e. Joules per distance covered. Now, let's assume on a slope this person tries to keep their heart rate the same as on flat ground, but part of that energy expenditure now goes to lifting the body to a higher altitude, I.e. increasing the potential energy". If you work that backwards, you might get a value for the speed that keeps the overall energy expenditure the same.

7. Apr 1, 2017

### rumborak

FYI, because it's horrendous weather in Boston and I'm bored, after a bit of calculations I got to the formula:

$$V(α) = \frac {1.4 m/s} {1+0.3 \tan {α}}$$

EDIT: So, at your asked 20 degrees, the speed would be 10% slower. Honestly, doesn't sound right, but I think that's because at 20 degrees already a lot of other factors come into play like your gait changing etc. Humans are evolutionarily optimized to burn little energy on flat ground. When it's no longer flat, less efficient muscle come into play that burn more energy.

Last edited: Apr 1, 2017
8. Apr 1, 2017

### rootone

Yes, the exact figure will be highly dependent on the individual's body frame, their metabolism, overall fitness, whether they have eaten recently, and a whole load more.
While you could come up with a formula for an idealized average person, that person most likely does not exist in reality,
so whatever theoretical formula you apply, in practice you'll have very wide error margins if testing it with actual people.

9. Apr 1, 2017

Staff Emeritus
First, 20 degrees is a huge angle! This is about what it looks like:

Second, if you ever are walking with a group of friends and hit a hill, you will immediately notice that you start to disperse until an effort is made to get back together. That alone says there is no universal formula applicable to all people. If there were, you would stay together.

10. Apr 1, 2017

### PeroK

What you need is Naismith's rule:

https://en.wikipedia.org/wiki/Naismith's_rule

11. Apr 1, 2017

### george95

Thank you for all the replies!!

Thank you Rumborak! What is the source of your formula?

12. Apr 1, 2017

### rootone

That is, 7.92 units of distance are equivalent to 1 unit of climb.
Rules of thumb like this are often handy.
While there is no theory to explain it, it's a statistic that satisfies most observations.

13. Apr 14, 2017

### george95

Thank you once again for the useful replies PeroK and rootone.

@rumborak what is the source of your formula? Where does it come from?

14. Apr 14, 2017

### rumborak

That formula really just comes from the assumptions I made in the preceding post to that. I think as is obvious, it's pretty off since it totally disagrees with Naismith's rule. It was really little more than a algebra exercise.

15. Apr 15, 2017

### george95

Thank you once again for the help Rumborak.