Rake vs headtube angle

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3/23/2017 5:38 PM

I was asked a question tonight and everyone around me could not come up with a difinitive answer, how does the rake on a fork affect the bikes steer tube angle? More specifically, if a frame has a 74 degree head tube and goes from a 32 mm offset to a 25 mm offset fork (disclaimer- the specific offset amounts are guesstimates) what would that change the steer tube angle to? We know it will become more 'responsive', we know the wheel base will become shorter, but what about the actual angle?

Thanks

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3/23/2017 5:52 PM
Edited Date/Time: 3/23/2017 5:59 PM

mistaare wrote:

I was asked a question tonight and everyone around me could not come up with a difinitive answer, how does the rake on a fork affect the bikes steer tube angle? More specifically, if a frame has a 74 degree head tube and goes from a 32 mm offset to a 25 mm offset fork (disclaimer- the specific offset amounts are guesstimates) what would that change the steer tube angle to? We know it will become more 'responsive', we know the wheel base will become shorter, but what about the actual angle?

Thanks

I've never thought about it but the HT angle is not really a good measurement. It depends on everything from fork rake to tyre pressure to tyre sizes to rider weight. I highly doubt just about any bike out there is running at the specified HT angle. This is a pretty good article: http://www.gsportbmx.co.uk/support/rideuktech/steering-geometry.html

EDIT: Now that I think about it, there wouldn't be much, if any change in HT angle. If you made a fork with horizontal dropouts, you could simulate several different offsets without changing the effective fork leg angle or the HT angle. Only things that would be different would be how quick it turns and how easy it is to get up over the nose.

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3/23/2017 5:54 PM

We brought up everything you mention, but if the ONLY thing that changes is the rake.

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3/23/2017 6:03 PM

mistaare wrote:

We brought up everything you mention, but if the ONLY thing that changes is the rake.

Don't know if you saw the edit on my previous post so:

If the only thing that changes is offset, there'd be no difference. If you made a fork with horizontal dropouts, you could simulate several different offsets without changing the effective fork leg angle or the HT angle. Only things that would be different would be how quick it turns and how easy it is to get up over the nose.

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My Sunday Soundwave V3 Build
Insta: @p.gibbons

"You can't educate pork"
- grumpySteve

"Life should not be a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather to skid in broadside in a cloud of smoke, thoroughly used up, totally worn out, and loudly proclaiming "Wow! What a Ride!""
- Hunter S. Thompson

3/23/2017 8:11 PM

Thanks man, sorry I did not see your edit. Great information. Appreciate it.

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3/24/2017 3:38 AM

It would mellow the ha a little, due to the shape of the fork legs, it would have to lift the front end of the bike to accommodate the wheel being further under the headtube. However, due to the shorter offset, that would compensate, so it would still feel more responsive. Probably anyway. I don't think any of this would be enough of a difference for anyone to really notice

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3/24/2017 1:53 PM
Edited Date/Time: 3/24/2017 2:13 PM

If you take p1p's model of a *perfectly horizontal offset plane (this is important for the calculations I did), you can calculate pretty much whatever you want with some basic algebra, geometry, and trig. Take the below picture (original courtesy of calfeedesign). All calculations rounded...

Photo

The knowns/constants are in black. I chose a 74° HT per the OP's original problem. I arbitrarily chose a 12" fork leg length. I chose a 25mm offset per one of the requested offsets from the OP's original problem.

If we know HT angle, we can plumb-line down from the bottom of the HT (or from anywhere, frankly as we're just looking at the base steering axis/HT angle) to get us a helpful right triangle. All angles of a triangle add up to 180°, so 180° - 74° - 90° = 16°

Since we already have the HT angle (74°) and the length of one side (fork leg length of 12"), we can use the sin trig function and a little algebra to get us length of the side that we plumb lined (the vertical line). sin (74°) = x/12" = 11.54"

Now that we have two sides of a right triangle, we'll use the Pythagorean Theorem to get the length of our last side for this part. √(12^2 - 11.54^2) = 3.29".

Great! We have all measurements and angles for inner/smaller triangle. Functionally, this would be like a 0 offset flatland fork, but we're talking offset forks, so let's move on to the 25mm offset...

From the smaller triangle we have a short side measurement of 3.29". 25mm == .98", so 3.29" + .98" = 4.27".

We already have the plumb line length of 11.54", so using the Pythagorean Theorem again, we can calculate the hypotenuse length of the "new" triangle. √(4.27^2 + 11.54^2) = 12.3".

Now we have all side lengths of the outer triangle (which represents the geometry for our 25mm offset). But we have only one angle, the right angle. Normal trig functions won't help here, so we have to move to the inverse trig functions. I used sin above, so I'll use the inverse sin now. sin-1 (11.54/12.3) = 69.75°.

Now that we have two angles of the 25mm offset triangle, we can calculate the final angle. 180° - 69.75° - 90° = 20.25°

And there you have it. Again, there are rounding errors, but you get the idea.

P.S: The short answer for a 32mm offset is an angle of 68.5° (replacing the 69.75° from before), so not much difference mathematically but definitely noticeable by the rider.

ETA: *If you take "classical" bicycle design, offset is actually the length perpendicular to the steering axis/HT angle. When you consider that, the functional HT angle will absolutely change with a different offset, which I think is what Steve was referring to. Not sure I care enough to figure that out right now, haha.

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3/24/2017 6:28 PM

GMGuinn wrote:

If you take p1p's model of a *perfectly horizontal offset plane (this is important for the calculations I did), you can calculate pretty much whatever you want with some basic algebra, geometry, and trig. Take the below picture (original courtesy of calfeedesign). All calculations rounded...

Photo

The knowns/constants are in black. I chose a 74° HT per the OP's original problem. I arbitrarily chose a 12" fork leg length. I chose a 25mm offset per one of the requested offsets from the OP's original problem.

If we know HT angle, we can plumb-line down from the bottom of the HT (or from anywhere, frankly as we're just looking at the base steering axis/HT angle) to get us a helpful right triangle. All angles of a triangle add up to 180°, so 180° - 74° - 90° = 16°

Since we already have the HT angle (74°) and the length of one side (fork leg length of 12"), we can use the sin trig function and a little algebra to get us length of the side that we plumb lined (the vertical line). sin (74°) = x/12" = 11.54"

Now that we have two sides of a right triangle, we'll use the Pythagorean Theorem to get the length of our last side for this part. √(12^2 - 11.54^2) = 3.29".

Great! We have all measurements and angles for inner/smaller triangle. Functionally, this would be like a 0 offset flatland fork, but we're talking offset forks, so let's move on to the 25mm offset...

From the smaller triangle we have a short side measurement of 3.29". 25mm == .98", so 3.29" + .98" = 4.27".

We already have the plumb line length of 11.54", so using the Pythagorean Theorem again, we can calculate the hypotenuse length of the "new" triangle. √(4.27^2 + 11.54^2) = 12.3".

Now we have all side lengths of the outer triangle (which represents the geometry for our 25mm offset). But we have only one angle, the right angle. Normal trig functions won't help here, so we have to move to the inverse trig functions. I used sin above, so I'll use the inverse sin now. sin-1 (11.54/12.3) = 69.75°.

Now that we have two angles of the 25mm offset triangle, we can calculate the final angle. 180° - 69.75° - 90° = 20.25°

And there you have it. Again, there are rounding errors, but you get the idea.

P.S: The short answer for a 32mm offset is an angle of 68.5° (replacing the 69.75° from before), so not much difference mathematically but definitely noticeable by the rider.

ETA: *If you take "classical" bicycle design, offset is actually the length perpendicular to the steering axis/HT angle. When you consider that, the functional HT angle will absolutely change with a different offset, which I think is what Steve was referring to. Not sure I care enough to figure that out right now, haha.

Wow, that's the most in-depth reply I've ever seen on here!

I'm quite surprised there's any change at all. I figured since it's offset horizontally but the fork leg angle and dropout height remain the same there'd be no difference at all. Are those results the effective angle between the headtube and axle center or the actual angle of the HT? I would check this myself but I've been riding for the past 12 hours so I'm far too tired to understand it.

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My Sunday Soundwave V3 Build
Insta: @p.gibbons

"You can't educate pork"
- grumpySteve

"Life should not be a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather to skid in broadside in a cloud of smoke, thoroughly used up, totally worn out, and loudly proclaiming "Wow! What a Ride!""
- Hunter S. Thompson

3/24/2017 8:46 PM

p1p1092 wrote:

Wow, that's the most in-depth reply I've ever seen on here!

I'm quite surprised there's any change at all. I figured since it's offset horizontally but the fork leg angle and dropout height remain the same there'd be no difference at all. Are those results the effective angle between the headtube and axle center or the actual angle of the HT? I would check this myself but I've been riding for the past 12 hours so I'm far too tired to understand it.

"Are those results the effective angle between the headtube and axle center[?]"

This! And you were right. As you stated up-thread, given your horizontal model, and all things remaining the same, there is no difference in HT angle. The HT angle with the horizontal model would remain what it was even if the horizontal offset went out (or in) 10 feet (ignoring flex/deformation,).

In my edit, I go on to mention that offset in a classical model is perpendicular to the HT angle/steering axis, in which case any change in offset with that model would not only change the angle of the HT, it would change the functional/effective geometry of the entire bike. Simply put, when you change the offset in the classical model, the whole bike will hinge on the rear axle up or down to some degree, thus changing every angle. I think maybe possibly this is what Steve was driving at, but I'm not entirely sure.

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