Cross What??

August 06, 2023

Do ebike wheels—with larger hubs, smaller rims, and increased loads—challenge the way we design? The physics are the same but priorities are a changed. One of the biggest differences is importance of spoke crossing pattern.

Cross pattern affects:

• Torque transmission—the transfer of power from hub to rim.
• Nipple angle at the rim—how much spokes bend at the thread end.
• Spoke length—each pattern requires a different, precise length.

In this machine, there is no suspension or rider standing so wheels take vertical shocks without assist. How best to build this wheel?

Hub
A nice feature of the e559 is a Bosch mid-drive motor. Integrated with the crank and front chainring, this unit hangs off the trike’s front end. Quite a different look! A benefit is the freedom to use any rear hub and our builder chose a Kindernay 7 speed. A cool design I’ve covered before.

Rim
They chose a 559/26” diameter DT EX-471 with 32 holes. Plus: easy to source. Minus: slightly weaker than 36 hole, a familiar and reasonable tradeoff.

Cross Pattern
The choice of pattern is open. As a powered disk brake wheel, radial (X0) is least desirable. X1 raises flags as torque transfer is only as effective as the spoke-to-hub angle.  As that angle approaches tangential, the hub drives the rim with diminishing spoke stress (stress = tension change with torque applied).

How to choose between cross 2 and 3?
About X2:

• Spokes 20mm shorter—saving the weight of 640mm of spoke.
• Rim side bracing is theoretically stiffer—shorter spokes arrive more directly to the rim.
• Nipple angle at the rim is less—less bend for the spoke = less breakage at the thread.

About X3:

• Spoke angle at the hub is more tangential—torque transfer is more efficient. Less tension change means less spoke stress during riding.
• 64cm of extra spoke weight is only 16g, not much in a wheel.
• Well designed rims and nipples can accommodate reasonable angles without spoke bending.

About both:

• Torque capacity of crossed wheels is 3–10 times the capacity of freehubs, gear teeth, and rider strength. Dismiss the concept of wheels failing from torque. It may appear to happen, but just as with chains, it is never sheer force that causes the failure. With wheels, there must be a simultaneous lateral or radial force and with chains, there is nearly always a connection issue.
• Side strength is primarily owed to rim stiffness and hub spacing. Cross pattern has hardly an affect.

Traditionally, the arguments for X3 win out. “Stiffer for torque” is appealing for most riders. However, a larger hub and smaller rim makes nipple angle greater than with old school wheels. Aren’t you curious to see the actual nipple angles before choosing?

Result: X2 generates an angle of 80.3º, X3 is 78.3º. Grin advises that angles over 80º are easy to lace and excellent for spoke life. Angles under 75º can be problematic for angle.

Clearly, these two choices are nearly identical. Here are two nipples sitting at a 2º difference in angle. Not much! Whenever you want to nerd out, defend your design, or confuse your customer, take a moment to get these angles. They help inform design and make the subject more understandable for all.

What to do in this case?

• Nipple angle (spoke fatigue at the threads) is an insignificant factor (2º).
• Weight gain/loss is insignificant (16g).
• Torque capacity/stiffness is overkill with either.

Our Catrike builder built 2 wheels. One X2 and one X3. How mischevious!

Whichever choice you would have made, I hope you feel vindicated!

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