Wheel Flop Calculator

Some bikes feel light and nimble at walking speeds. Others seem to fall inwards on every slow turn with the handlebars pointing into the corner as if the front wheel had a mind of its own. This pull has a name and a number: "trail". When you turn the bars from straight ahead, the sloping fork blades cause the bike's frame to tilt slightly downwards while gravity pulls it continuously down and inwards. This calculator can accurately compute the front wheel drop for any trail value and fork blade angle or conversely determine the frame geometry that produces a desired feel.

What is a trail?

"Trail" is the phenomenon that the bike frame lowers when the handlebars are turned from straight ahead position. Because of the fork rake being angled back and not vertical, turning the handlebars causes the front wheel to turn but also move down, lowering the whole front part of the bike. The "trail" value is expressed as a number: the amount that the fork moves down when the handlebars are turned by a quarter of a circle, or 90 degrees, from straight ahead. The larger this value is, the longer the lever arm over which gravity pulls to turn into a corner. So bikes with smaller head tube angles and more trail feel heavy in the park but stable on motorways. The same geometry creates both these properties.

How to use this calculator:

Enter the trail value to calculate front wheel drop. The fork rake is set at 72 degrees by default which is a typical angle for road bikes, so you will only get a result based on the trail value; you can change the angle to suit your bike. Each field has a separate unit selector, so you can enter the trail in millimeters or inches and the angle in degrees or radians. Conversely, you can leave any of the fields blank: enter the desired front wheel drop and trail to get back the fork rake, or enter the front wheel drop and the fork rake to get back the trail. If you don't know the trail value, open the geometry level and determine the parameters based on wheel diameter and overhang.

Understanding of formula.

The trail value is equal to the product of the handlebar distance and the sine of the head angle, multiplied by the cosine of that same value.

The same relationship can be more compactly expressed using double-angle formulae, which makes its form clearer:

As you can see, the maximum trail is at most half of the handlebar distance and is achieved when the head angle is 45 degrees. Let's consider a bike with a handlebar distance of 60 mm and a head angle of 72 degrees:

So the fork lowers about 17.6mm when the handlebar is turned a quarter of a turn. The following table shows each symbol and its example values.

Should the head angle be measured horizontally or vertically?

This formula has an interesting property: since the result of sine times cosine does not change if you swap the angles, sin(72) x cos(72) = sin(18) x cos(18). In bicycle terms, the head angle is measured horizontally, so it's about 72 degrees on a road bike. In motorcycle terms, the fork angle is measured vertically, so the same handlebar angle would show about 18 degrees. Both measurements give the same trail value, so there's no error in entering the angle: whichever definition you use for your spec sheet, it will give the same numerical result.

How is the trail determined?

The trail is not a freely adjustable parameter. It is influenced by three factors: the wheel radius, the steering angle and the distance by which the fork displaces the axle ahead of the head of the front fork. This displacement is referred to as the fork set or fork cut. The values for the trail listed in the geometry table are:

R is the wheel radius, O is the fork offset. The larger the wheel radius or the smaller the steering angle, the longer the trail; the larger the fork offset, the shorter the trail. There's also a shorter measure called mechanical trail: it's the distance from the contact patch to the head of the steering axle, measured in a direction perpendicular to the axis, not along the ground. It is equal to R x cos(theta) minus the fork offset and represents the effective lever that causes the self-centering of the steering. This calculator shows both values at once.

Why is the steering wheel turned to the curve?

The trail indicates how much a wheel will drop on a quarter turn of the handlebars. However, at smaller steering angles there is also less droop in the fork and follows the relationship f multiplied by (1 minus the cosine of the steering angle). This curve is nearly flat near the centerline but becomes steeper at the end of maximum steer. So a slight wobble of the bars near straight ahead will cause little movement of the fork, while the last short bit of tight turn causes the fork to drop quickly. As the fork drops, gravity acts and creates a torque that is equal to the product of the front wheel load, trail, and sine of the steering angle. This is the automatic steering behavior you feel at low speeds as the bars try to continue into the curve. At higher speeds however, the gyroscopic stability of the spinning front wheels and the inherent balance of the bike outweigh this effect. This explains why the same bike will tend to fall over at slow speeds while it tracks straight at speed. In the control area you can see both the droop and torque for any steering angle you select.

How do you pick your values?

There is no one correct value; it always depends on the trade-off between various factors. The magazine "Bicycle Quarterly" described this very aptly: Bicycles with a too small head angle respond sluggishly to steering movements, while bicycles with a too large head angle tend to deviate from their original course at low and medium speeds. Road bike frames often use larger steerer angles and shorter trail values in order to reduce the head angle and speed up the steering movement, while simultaneously accepting some nervousness at high speeds. The geometry of touring and cruiser bikes is more relaxed and longer; by increasing the head angle a calmer riding behavior is achieved that remains stable even without hands on the handlebars, albeit at the cost of heavier steering at low speeds. Also the weight distribution in front plays an important role: A heavier front wheel or a fully packed handlebar bag reinforces the effect of the head angle and creates a stronger pull.

Where is this value used?

Frame designers calculate this ratio before they even cut a tube set because once the head angle and trail are welded in place, only the tires and fork provide any fine-tuning options. Custom motorcycle builders also check this value when increasing the steering angle since longer telescopic forks can increase the steering angle so much that low-speed maneuvering on a parking lot becomes a real physical challenge. Mechanics and bike fitters use it to explain why two bikes with similar specs can ride so differently if one has more weight up front. Conversely, you can also easily calculate this value: If you want to know what head angle is required to achieve a given trail for a particular steering angle, just enter the desired steering angle and the result will be displayed immediately.