Understanding the Physics of Running: Treadmill vs Outdoor Runs

Introduction

Most current research focuses on runner’s performance on a treadmill rather than outdoors. One should, however, be aware of the differences between running on a treadmill and running outdoors. It seems that both activities are similar. Yet, there are different amounts of work done and different physics of running in each.

I tried running both on a treadmill and outdoors and I noticed that it’s much harder to run 1.8 km outdoors than to run the same distance on a treadmill. Roughly speaking, I can spend 23 minutes running 2.6 km on a treadmill at an average of 7 km/h and still feel fresh. Still, I spend 13 minutes running 1.8 km outdoors at an average of 9 km/h and feel really exhausted and out of breath at the end. I asked myself a question about the differences between both types of running and why outdoor running feels much harder.

For the purpose of the next analysis let’s define certain terms and measurements:

Stride – entire cycle of movement that occurs as a person takes a step with each leg. It includes the phases starting from the moment one foot contacts the ground. The cycle ends when that same foot contacts the ground again. One stride for a man 183cm tall running at 2.5 m/s is approximately 2.0 m.

Bounce – vertical rise of a person’s body with each stride while running. The average bounce is approximately 7.5 cm (0.075 m when running at 2.5 m/s)

Length of track – 1800 m (or 1.8 km)

Running speed – 2.5 m/s (or 9 km/h)

Elevation – 6 meters.

Mass – 70 kg

Physics of Running on a Treadmill – Bouncing

Running on a treadmill involves pushing yourself up twice for every stride. To find work done by bouncing up and down along a distance of 1800 m:

1. Potential Energy per bounce (PE1) = mgh = 70*9.8*0.075 = 51.45 J
2. Potential Energy per stride (PE2)  = 2*PE1 = 102.9 J
3. Potential Energy per track = 1800/2.0 * PE2 = 92610 J

Notice that increase in speed generally results in an increased stride length. The number of strides per track goes down and the total work by bouncing decreases.

Physics of Running Outdoors

Running outdoors involves many more factors than running on a treadmill. Bouncing is a common mechanic of running in both types. Thus, we can apply the same calculations for work done by bouncing to running outdoors as well. 

Potential Energy per track = 92610 J

Extra factors in outdoor runs are Hills, Change of Direction, Air Resistance and Braking. Which one of these factors contribute the most to work done by a person? We will answer that question next.

Outdoor Run – Hills

While running outdoors, you exert effort to lift yourself up when running uphill. You let gravity bring you down when running downhill. We use 6 m for an average elevation gain for a track of 1800 m. 

Potential Energy = mgh = 70*9.8*6 = 4116 J

Note that you never do work on lifting yourself up when running on a treadmill. There are no hills, and you stay stationary with respect to the ground. Running uphill and elevation gain is only relevant to running outdoors.

Outdoor Run – Direction

When running outdoors you always do more work changing direction of your movement. Let’s simplify a task by considering what happens to your kinetic energy when you take a 90-degree turn. For a turn, you must bring your onward velocity to zero. Then, you must accelerate along the perpendicular direction to reach the target speed. Thus, the change in kinetic energy is twice that of your current kinetic energy:

As you have understood, there is no direction change running on a treadmill. Direction changes only when running along a non-straight path outdoors.

Outdoor Run – Air Resistance

The drag force acting on a person while running outdoors depends on their speed and the air density. It also depends on their body shape and the surface area facing the wind. The drag force Fd can be calculated using the formula:

Where:

Cd is the drag coefficient (for an average human running, typically between 1.0 and 1.3)

A is the frontal area of the runner facing the wind (around 0.5 – 0.7 square meters for most adults).

P is the air density (about 1.225 kg/m^3 at sea level)

V is the relative velocity of the runner with respect to the air (i.e. the runner’s speed plus or minus any wind speed)

Let’s calculate the drag force for a runner moving at 2.5 m/s assuming no wind:

Cd = 1.2

A=0.6 m^2

P=1.225 kg/m^3

v=2.5 m/s

We can find work done by a person running outdoors against the air as:

Work = Fd * d = 5.5 * 1800 = 9922.5 J

Where F is the drag force and d is the distance.

Outdoor Run – Braking

Outdoors you use friction to move your body ahead. So that friction will increase your body’s velocity. With each swing of your leg, your leg goes ahead and grabs the ground in front of you. The moment it applies a force on the ground, the friction will act on the leg to bring it back. But this friction also partly slows your whole body down.

The amount a person slows down with each ground contact while running varies. It depends on the runner’s speed, form, and efficiency. This deceleration can be estimated as a slight reduction in forward velocity. It is usually on the order of about 5-10% at the point of impact. For a person running at 2.5 m/s this is equal to roughly 0.2 m/s. The runner recovers this loss when they push off from the ground. They regain their speed and sometimes even add a bit more.

Physics of Running at 2.5 m/s:

The total work done by your body to decelerate from 2.5 m/s to 2.3 m/s and then accelerate back to 2.5 m/s is:

Work done per cycle = Loss in Kinetic Energy (KE1) + Gain in Kinetic Energy (KE2) = (Kinetic Energy at max speed – Kinetic Energy at reduced speed) * 2 =

At each stride you loss and gain kinetic energy twice, therefore total work done per stride is:

Work per stride = Work done per cycle * 2 = 67.2 * 2 = 134.4 J

If we now consider how much work you do by braking and accelerating along a 1800 m track:

Total Work = Length of Track / Length of Stride * Work per stride = 1800/2.0 * 134.4 = 120960 J

So, running outdoors will add extra 120960 J of work needed to apply braking. To compare which factor causes you to do extra work lets create a table:

In the table we see that bouncing and braking constitute (92,610 + 120,960) / (Total) = 93.6% of total work in running outdoors. When compared with treadmill, running outdoors do (92,610 + 120,960) / (92610) = 2.3 times more work than on a treadmill. No surprise it feels harder!

Effects of other factors such as hills, direction and air resistance account only for (4116 + 437.5 + 9922.5)/(Total) = 6.3% of total work.

Physics of Running at 1.25m/s

Let’s see what happens to the work done for braking when you slow down your speed in half from 2.5 m/s to 1.25 m/s when running outdoors:

Stride length for a man 183 cm tall running at 1.25 m/s is 1.1 m.

The total work done by your body to decelerate from 1.25 m/s to 1.15 m/s (8% reduction in speed) and then accelerate back to 1.25 m/s is:

Work done per cycle = Loss in Kinetic Energy (KE1) + Gain in Kinetic Energy (KE2) = (Kinetic Energy at max speed – Kinetic Energy at reduced speed) * 2 =

At each stride you loss and gain kinetic energy twice, therefore total work done per stride is:

Work per stride = Work done per cycle * 2 = 16.8 * 2 = 33.6 J

If we now consider how much work you do by braking and accelerating along a 1800 m track:

Total Work = Length of Track / Length of Stride * Work per stride = 1800/1.1 * 33.6 = 54980 J

This is 54980 /120960= 0.455, more than half less work done by braking at only half speed (1.25 m/s rather than 2.5 m/s).

New estimate for work done by bouncing:

Potential Energy per bounce (PE1) = mgh = 70*9.8*0.065 = 44.59 J

Potential Energy per stride (PE2)  = 2*PE1 = 89.18 J

Potential Energy per track = 1800/1.1 * PE2 = 145930 J

The stride is slightly smaller at half speed so there are more bounces per track and total bouncing work rises. The bounce height, or vertical oscillation, is slightly smaller for running at half speed so the total bouncing work slightly decreases. The new estimates for running at half speed are:

Ratio of work of running at 1.25 m/s to work of running at 2.5 m/s is (145930 + 54980)/(92610 + 120960) = 0.94 times less work. So, by running at half speed you decrease your power (work over time) and also decrease the total work per track. If you are tired running outdoors, you can simply slow down as reducing your speed will greatly reduce the required work. This physics of running is a good thing to be aware of and a good strategy to utilize.

What about braking when running on a treadmill?

There is no braking factor when running on a treadmill in the way that it exists during outdoor running. Braking makes physics of running outdoors unique. When running outdoors, a person generates forward momentum. They have to counteract it with each stride to control their speed and stability. This generates a slight “braking force” with each footfall to decelerate forward motion before propelling forward again.

On a treadmill, however, the belt moves underneath the runner at a constant speed. The runner does not propel their body forward in the same way. Instead, the runner’s legs are simply keeping up with the moving belt. There is little to no braking force involved. The experience can feel different because the runner doesn’t have to generate and control forward momentum.

This lack of a braking force on a treadmill is one reason running on a treadmill can feel easier. It may be less demanding than running outdoors, especially at the same pace. 

Findings on Mechanics of Running

The following table provides summaries of findings in this article:

Summary

This article presented detailed analysis of the differences in mechanics and energy expenditure between treadmill and outdoor running. It explored why outdoor running often feels more demanding, despite covering the same distance or maintaining similar speeds. Most energy expenditure for outdoor run is due to bouncing and braking factors. For treadmill running only bouncing factor is present. Hopefully, knowing what to expect from each type of running will help you prepare for the run.