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:
- Potential Energy per bounce (PE1) = mgh = 70*9.8*0.075 = 51.45 J
- Potential Energy per stride (PE2) = 2*PE1 = 102.9 J
- 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 – Slowing Down with Each Stride
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.
Running on Treadmill (left) vs Running Outdoors (right).
The forces that act on the body in Treadmill and Outdoor runs are same for vertical movement (bouncing) but different for horizontal movement. On treadmill the body is static relevant to the treadmill hence there is no work done on it. The only part that moves with respect to the treadmill are the legs (feet, to be precise). In this case, the force Fs acts on the front foot to bring it back. It acts until the foot gains speed equal to the speed of the belt. Thus, the energy required to stop one foot and bring it forward is the following:
For running speed of 2.5m/s, the energy is the following:
Now consider what happens in case of an outdoor run. Now the whole body moves with respect to the ground. The force Fg that acts when front foot touches the ground has both vertical and horizontal components. Horizontal component Fs for outdoors acts on the whole body, slowing it down in addition to bringing the front foot back. The whole body loses speed with energy that is lost calculated as follows:
The amount a person slows down with each ground contact while running varies. It depends on the runner’s speed, form, and efficiency. 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.
Now the lost energy is calculated as follows:
Comparing energies from treadmill run and outdoors run we find the following results:
For a person of weight 70kg, the total mass of one foot is approximately 1.5% of body mass, that is 1.05kg.
| Energy in one foot (For Treadmill run as well as Outdoors run) | Energy lost by slowing body down (Outdoors Run) |
| 1.05*2.5^2/2 = 3.3 J | 67.2 J (see next section) |
We already see that for a cycle, energy requirements for outdoors run are (67.2+3.3)/3.3=21 times greater than for treadmill run!
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 countering slowing down for the whole body. To compare which factor causes you to do extra work lets create a table:
| Factor (for man 183 cm tall running at 2.5 m/s) | Work (J) |
| Bouncing (Treadmill and Outdoors) | 92,610 |
| Foot movement (Treadmill and Outdoors) | 5,760 (120,960/21) |
| Hills (Outdoors only) | 4,116 |
| Direction (Outdoors only) | 437.5 |
| Air Resistance (Outdoors only) | 9,922.5 |
| Slowing Down (Outdoors only) | 120,960 |
| Total (Outdoors) | 233,806 |
| Total (Treadmill) | 98,370 |
In the table we see that bouncing and slowing down constitute (92,610 + 120,960) / (Total) = 91.3% of total work in running outdoors. When compared with treadmill, running outdoors do (92,610 + 120,960) / (92610) = 2.37 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) = 6.2% of total work.
Physics of Running at 1.25m/s
Let’s see what happens to the work done for slowing down 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 slowing down 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. The new estimates for running at half speed are:
| Factor (for man 183 cm tall running at 1.25 m/s) | Work (J) |
| Bouncing (Outdoors) | 145,930 |
| Slowing Down (Outdoors only) | 54,980 |
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. The total work done decreases by only 6%. This is unsurprising, since the person runs same distance in total. What changes significantly is the power. By running at half speed you decrease your power (work over time). If you are tired running outdoors, you can simply slow down as reducing your speed will greatly reduce the required power. This physics of running is a good thing to be aware of and a good strategy to utilize.
Findings on Mechanics of Running
The following table provides summaries of findings in this article:
| Physics of Running Outdoors | Physics of Running on a Treadmill |
| Due to slowing down, running outdoors requires about 2.37 times more work than running on a treadmill. | Running on a treadmill requires only work by bouncing and movement of feet. |
| Slowing down and bouncing factors all alone account for about 91.3% of total work done when running outdoors. | Work by bouncing accounts for 94% of total work. |
| Effect of hills, air resistance and direction changes in outdoor running is only 6.2% of total work. This is insignificantly small compared to the effects of slowing down and bouncing combined. | There are no additional factors. |
| In outdoors running, one can reduce total work done by 6% by slowing down from 2.5 m/s to 1.25 m/s. In addition, slowing down will reduce the power so you will output less work per second for longer time. | Work by bouncing decreases when you increase running speed. |
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 slowing down. For treadmill running only bouncing factor is significant. Hopefully, knowing what to expect from each type of running will help you better prepare for the run.