## The Connection Between The Seat Tube Angle and Saddle Setback Explained (graphs)

This post explains the connection between the seat tube angle and the position of the saddle.

There are two seat tube angles – the effective seat tube angle and the actual seat tube angle.

The actual seat tube angle (STA) is formed by a line passing through the bottom bracket and another one going through the seat tube (image below).

The saddle setback has no influence on the actual seat tube angle.

In this case, the position of the saddle is irrelevant because the angle is derived from the seat tube, not the saddle.

The effective seat tube angle (ESTA) is formed by a horizontal line passing through the bottom bracket and another line that passes through the middle of the junction where the seat post connects to the saddle.

The position of the saddle directly influences the effective seat tube angle. Moving the saddle towards the front wheel steepens the ESTA; moving it towards the rear wheel slackens the ESTA.

The saddle setback is the horizontal distance between the center of the bottom bracket and the saddle’s nose. (image below)

Consequently, saddle setback directly influences the effective seat tube angle.

## Calculating The “Relationship” Between Saddle Setback and The Seat Tube Angle

If one uses trigonometry, it’s possible to make calculations revealing the link between the effective seat tube angle and the saddle setback.

To find out the link between the ESTA and the saddle setback, we need the following data:

• The saddle height (there are different ways to measure it, but in this case, I am using the shortest distance between the middle of the bottom bracket and the top of the saddle).
• The effective seat tube angle

The graph below will appear somewhat complicated at first, but it’s not all that complex once you know what you’re looking at.

The saddle height, a line perpendicular to the bottom bracket, and a line connecting them via a 90-degree angle form a right triangle called ABC.

• The saddle height or the AC side is the hypotenuse (the longest line of a right triangle).
• The CB side includes the saddle setback.

The angle between the AB and the CB side is 90 degrees. If we know the effective seat tube angle we can find the A1 angle (the angle between AC and AB).

How?

The effective seat tube angle + angle A1 forms 90 degrees. Thus, if we extract the effective seat tube angle from 90°, we can find the A1 angle.

Once we have the A1 angle, we can find the C1 angle. The sum of all angles in a triangle is 180 degrees. Thus, if we know two angles we can easily find the third. In this case, the C1 angle = 180° – 90° – A1.

Once we have all the angles and the hypotenuse, we can find the length of the other sides.

The CB side indicates the saddle setback changes.

If we change the effective seat tube angle, we also change the A1 angle and with it the CB length. The change in CB length indicates the setback changes too.

Let’s make some calculations with hypothetical data.

• AC (saddle height) = 68cm
• ESTA = 73°.

If the ESTA is 73°, then the A1 angle is 90°-73° = 17°.

If the A1 angle is 17°, the C1 angle is 90°-17°=73° (The ESTA angle and the C1 angle will always be the same).

So, we have a right triangle with the following data:

Hypothenuse = 68cm; Angles – 90°, 73°, 17°.

You can use formulas to find the sides yourself or simply put the data in a calculator.

So, originally, the AB side is 65cm and the CB side is 19.88cm.

If we steepen the seat tube angle from 73° to 74.5°, the data changes to:

So, steepening the effective seat tube angle by 1.5° would result in a 1.72cm reduction of the CB side.

In this case, the CB side is decreased from 19.88cm to 18.17cm.

If we want to preserve the original saddle set back we will have to move the saddle backward by about 1.72cm.

Doing the opposite, namely slackening the ESTA by 1.5° results in a 1.62cm increase of the CB side.

Thus, if we want to preserve the original saddle setback, we have to move the saddle forward by 1.62cm.

## Conclusions

• The effective seat tube angle directly affects the saddle setback.
• А 1° change of the effective seat tube angle results in about a 1cm difference to the saddle setback.
• Steeping the seat tube angle decreases the saddle setback.
• Slackening the seat tube angle increases the saddle setback.