Adapting Mountain Bike Fit to Drop Bars

Lee McCormack has a great big idea for a starting point on mountain bike fit - RAD. You take your height, multiply it by a constant number, and that gives a Rider Area Distance number. You'll then measure a line from the bottom bracket, and it should end where your grips are. Easy! Can we apply this to drop bars? Yes!

Now, the linked fit guideline is obviously a huge simplification - your exact bike fit will be determined by much finer measurements than mere height. You need to know your inseam, leg length, arm lenth, forearm length, shoulder width, etc to calculate exactly what's up. And even then, it's just a starting point - you may find that you want a more upright setup, or you might want to be a bit more aggressive.

You may try to measure a straight line from the bottom bracket to where your grips actually exist in 3D space. I did this and was dismayed that I must need an XS bike! Instead, you want to measure a line along the bike frame. When the line stops, that's where your grips need to be, if you were on handlebars that were 0mm wide. 

Let's get more mathematical. Take a picture of your bike from a horizontal view. The top picture in this article is a great example. Now, you and I both know that the bike has handlebars that are wider than 0mm. But in the picture, they look flat - it's impossible to tell just how wide they are. The RAD is the distance of the line we draw if we collapse the 3D bike into a 2D plane and then draw a line from BB to grips.

A critical thinker will note that this number can be used to give all kinds of bizarre grip positions. The RAD line is actually the radius of a circle centered on the bottom bracket, and if you wanted, you could place the handlebars straight up, behind the bike, under the bike, etc and be within the parameters of the RAD guidance.

Now, that's obviously stupid, and not what Lee is recommending. He hints that there's another aspect: the exact angle (relative to the ground) described as Rider Area Angle in Degrees (RAAD). There is a sensible range of angles that will work depending on your skill, riding style, and flexibility. So rather than describing an absurd circle, this line will instead describe a sensible arc of fit starting points. The article lists 55 degrees as the low end for XC bikes and 63 degrees as the high end for DH bikes, which most people liking something in the 58-60 range.

There's a final piece to the puzzle - finding a starting point for handlebar width. Again, Lee has you multiply your height by a constant to figure out how wide your bars should be - a rough estimate starting point, and if you want better guidelines, go buy a fitting from the man. Wider handlebars effectively shorten your arms by having them stretch more to your sides, which causes you to lean over more.

Let's apply these figures to drop bars. Note that I am not a biomechanics expert, just a nerd that likes spreadsheets and geometry. We want to determine the distance from bottom bracket to the grips. We can solve this with some geometry.

The first thing we'll want to do is expand that 2D image into a 3D projection. We're going to unlock the RAD circle into a RAD sphere. We have two variables h for your height and d for the RAAD angle, and then we have two constants W for handlebar width and R for the RAD constant. The position of the grips on the 2D plane from the BB is hR. The position of the grips extending out from this 2D plane is a line of length half-grip = hW/2 - half the grip width. We now have two triangles: one in the plane of the bike, and one in the plane of the handlebars. Both of these triangles have a vertex on the bottom bracket as well as the middle of the handlebars.

Let's name them and be very precise about their points/segments:

• Triangle RAD:
• A - Bottom Bracket. Angle is RAAD.
• B - Grip on the 2D plane of the bike. 
• The segment AB is the RAD.
• C - Directly down from B, directly across from A, 90 degree angle
• The segment AC is the reach of the bike.
• The segment BC is the stack of the bike.
• Triangle Handlebars (HB):
• A - Actual grip location.
• B - Grip location projected towards the plane of the bike frame. 90 degree angle.
• C - Directly down from B, meeting point RAD-C.
• This segment BC is also the stack of the bike.
• Segment AB is half of the handlebar width.

We can get a triangular pyramid if we draw another triangle that connects these two. We want the length of the line from the grips to the bottom bracket. We know that the angle from the ground to the grips is 90 degrees, and we have the RAAD angle for the BB to the handlebars as the variable d. So our final triangle is:

• Triangle Grip Distance (TGP):
• A - Grip
• B - Bottom Bracket
• C - Same as point C in the above two triangles.

So we'll end up needing to solve the length of segment TGP-AB in order to free our RADness. 

We can determine how far forward the grips must be (the effective reach - frame + stem + bars) by solving the length of the bottom edge of this triangle.

We have two determined angles and we can calculate the third - it will be 180 - 90 - d. We have one segment length - the hypotenuse of this triangle. From this, the reach will be equal to reach = (hR * sin (180 - 90 - d)) / sin 90. 

Next, we want to determine the angle from the bottom bracket to the grips, horizontally. We flatten our MathBike again, this time looking from the top down. We know the reach from the last paragraph, and we know the effective width of our handlebars: half-grip = hW/2. This is a right triangle, with a 90 degree angle from the middle of the bike to the grips. Since we know the right angle and both sides, we can calculate the angle using arcsin( a / c ) where a = half-grip and c = reach.

We're almost there. We've solved the two triangles. Now we can complete the tetrahedron with the law of sines for tetrahedra. 

Maybe I'll finish this in "Part Two," but right now I want to get this out because it's actually pretty useful!