Project Introduction: Malicious Compliance (sorry for the bad pun) is an exploration in increasing “comfortable” compliance on a bicycle frame. I designed and built two frames with identical geometry but very different rear-end designs. My ultimate goal is to identify frame design characteristics that improve riding comfort for touring and cargo bikes.
The control frame is a conventional double-diamond frame with the seatstays terminating on the seattube near the toptube junction. The flex frame has long seatstays that terminate onto a doubler plate welded to the downtube. Initial FEA studies indicate that the flex design has significantly more vertical seat deflection for in-plane loads and de-couples the saddle and rear axle from lateral contact patch loads. During torsional BB loads (from pedaling), the flex seattube has considerably more lateral deflection than its double-diamond counterpart.
I’m unsure how these differences in frame stiffness will translate to real-world ride feel. My original hypothesis was that vertical, in-plane compliance was the primary characteristic of a comfortable steel bike. However, after seeing Nolan’s vertical compliance video and reading some of Daniel Yang’s thoughts, it appears that lateral compliance/flex may be the driving factor for a comfortable frame. However, Nolan collected his data when descending and out-of-the-saddle. I’m interested in seeing if vertical compliance has a greater effect when seated and pedaling on rough roads.
I will be riding both frames and comparing their performance two ways:
Butt-Dyno (tried and true!)
Yost Labs accelerometer, similar to what Nolan used in his video.
I’m excited to see what the correlation is between subjective ride feel and analytical data.
The Fork…
I made a raked fork to pair with my flex/conventional frames. I ended up choosing a tapered, raked fork blade for two reasons:
Minimize x-deflection (towards the rear wheel) under tractive forces developed during braking (in retrospect, a better setup would have been also including a remote moment / force to simulate the brake caliper load)
Maximize z-deflection from normal loads.
I ran FEA simulations for the following configurations:
Unicrown fork with straight legs (at an angle to achieve desired offset)
Segmented fork with circular legs (at an angle to achieve desired offset)
Segmented fork with ovalized legs (at an angle to achieve desired offset)
Segmented + raked fork
Ultimately, I found the raked fork to be the best combination of the two target parameters.
Below are the simulation results for vertical force in the x-direction (left) and z-direction (right). We see that the unicrown and raked forks have around 27% and 18% more vertical deflection compared to the two segmented, straight-blade forks.
Note: The upper bridge tubes (connecting the steerer to the blades) for the segmented/raked forks is a 1”, or 25.4mm, circular tube. The unicrown fork has a 28x20mm ovalized cross section in this region.
Let’s consider the torsional constant of these two cross sections. Using formulas from StructX, the values for the two cross-sections are:
J unicrown= 10,000 mm4
J circle= 13,800 mm4
So… the torsional constant (and to simplify, stiffness) is 38% higher for the segmented forks with the circular bridge! Perhaps this helps explain the large difference in deflection.
I also think the geometry of the raked fork - specifically the offset from the applied axle force which increases the moment developed in the blade cross section - makes it more vertically “compliant” than its straight blade counterparts.
Below are the simulation results for braking force in the x-direction (left) and z-direction (right). We see that the unicrown fork is significantly less stiff than the other three designs in both the x and z directions. All the other forks appear similar in stiffness with the raked variant being marginally stiffest in the x-direction.
I’d use reasoning similar to the vertical deflection (the circular bridge has higher torsional stiffness) to explain why the unicrown fork experiences so much more deflection under braking compared to the other designs.
Build Process!
I will be posting several videos covering the design, fabrication, and testing of the two frames.