# Calculating Maximum Speed of a Bike Downhill

• tycon69
In summary, the maximum speed a bike can reach down a 45 degree hill is 132 mph if the rider and bike are combined weight of 210 lbs and the bike has 20 inch diameter wheels.
tycon69
Well, let's say we have a bike and we wanted to see the maximum speed that the bike would reach down a hill. Let's say that the combined weight of the rider and the bike is 210 lbs. The diameter of the wheels is about 20 inches and the hill is 45 degrees steep. The hill is smooth and has just enough surface tension to hold the bike up. The hill extends infinitively or however long it needs to be for the bike to reach maximum speed at these conditions. I was wondering if this Maximum Speed could be determined mathematically. I have yet to take a physics course, so i really know nothing of mechanics or the such, and i was wondering if someone could show me how we would calculate such a problem.

Under such conditions, the maximum speed is a terminal velocity determined by air resistance.

With an aerodynamic riding suit, unfaired bicycle downhill record on snow is 132mph, on dirt (actually lava bed from volcano), 107mph (bike broke, but rider survived). I don't know how steep the hills were though.

Just a conceptual comment, the bike will never actually reach its terminal (maximal velocity) in a finite time, instead the bike's velocity will come arbitrarily close to the terminal velocity. If we assume rectilinear motion (the bike travels in a straight line down the hill), then finding the terminal velocity involves solving an ODE of the form,

$$m\ddot{x} = mg\sin\theta - k\left(\dot{x}\right)^2 = 0$$

Which has quite nice solutions (assuming the density of air remains approximately constant). To determine the value of k, we would need information on both the cross-sectional area of the bike/rider and the numerical drag coefficient (which we could approximate). If you like I could detail the solution here, but I'm not sure how useful it would be if you haven't done any calculus before.

## What is the formula for calculating maximum speed of a bike downhill?

The formula for calculating maximum speed of a bike downhill is Vmax = √(2gh), where Vmax is the maximum speed, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the hill in meters.

## Why is it important to calculate maximum speed of a bike downhill?

Calculating maximum speed of a bike downhill is important for safety reasons. It allows the rider to anticipate and prepare for potential hazards such as sharp turns or obstacles on the road. It also helps in choosing the appropriate gear and braking technique to maintain control and avoid accidents.

## What factors can affect the maximum speed of a bike downhill?

The maximum speed of a bike downhill can be affected by various factors such as the weight of the rider and the bike, the aerodynamics of the bike and rider, the condition and steepness of the road, and external factors like wind and friction.

## Is it possible to reach a speed faster than the calculated maximum speed?

Yes, it is possible to reach a speed faster than the calculated maximum speed. The calculated maximum speed is based on ideal conditions and assumes that the rider maintains a straight path without any external factors affecting the speed. Factors such as pedaling or a tailwind can result in a higher speed.

## How can the maximum speed of a bike downhill be increased?

The maximum speed of a bike downhill can be increased by reducing the weight of the rider and the bike, improving the aerodynamics of the bike and rider, choosing a steeper and smoother road, and minimizing external factors such as wind resistance and friction. Additionally, pedaling and using an aerodynamic riding position can also increase the maximum speed.

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