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October 31, 2016 8 Comments
There’s hardly a more multi-tasking structure in all of engineering than the bicycle wheel. All its components are mutually dependent and interactive. Then no surprise tire pressure affects spoke tension. Here’s first of a 2-part discussion of this phenomenon, that is reaching a worrying scale in today’s wheels. Inflate a clincher to 90psi (6 bar) and you may see tension drop 20-50%. Why? Is tension drop bad? Should wheels be over tightened to compensate?
Today we focus on rims. What is their role in this dynamic? Why is this news? Bikes have been rolling on inflated tires for over a century!
Rims are the interface between tire pressure and spoke tension. They are elastic, changing shape in response to tire pressure. Key is understanding the very different forces clincher tires exert compared to tubulars. Clincher forces are major, tubular, minor. High performance clinchers are a relatively recent development and some pieces of their story are not yet in synch with the rest. This is the key to tension drop.
Other vehicle (auto, truck, plane) wheels do not have to be so light. They meet clincher tire forces with mass required for their high payload. For bicycles wheels there is no such escape.
Clincher rims see two substantial tire forces:
(1) Outward pressure on the rim bead hook that must be resisted or the rim explodes. We see this if brake tracks are excessively worn and the rim blows off its bead hook.
(2) Inward force (towards the wheel center) as air presses on the rim bed.
With tubulars, #1 and #2 are missing because the hoop of the sewed together tire casing carries those forces.
Clincher bead pressure (#1), can be estimated. Think 90psi (6.3kgf/cm^2). That force is exerted on the rim over its total bead area. Typical bead height is 6-7mm. Rim circumference (for 700C) is about 196cm. Total area of each bead hook:
196cm X 0.7cm = 137cm^2
With inflation of 6.3kgf/cm^2:
137cm^2 X 6.3kgf/cm^2 = 864kg pressure on each bead hook
This staggering force deforms rims. Rims with parallel brake tracks expand 2-5deg. Brakes accommodate the angle with adjustment and pad shape. Aluminum accommodates by elastically deforming but not prematurely failing. Measure this yourself: place a vernier across brake tracks before and after inflation. Angle changes!
The bigger issue for the wheel is the effect on the rest of the rim. When the bead hook is forced outwards, it effectively pivots at the web that forms the bead shelves. Rim sidewall below the brake track is rotated inward. creating additional sidewall length, enough to lower the nipple slightly towards the hub. Steel spokes are elastic, but small change in length make measurable change in tension.
A clincher rim splays open 2-5deg, the rim becomes deeper, lowering spoke tension. To resist this deformation and unhelpful tension decrease:
(1) Use tubulars, they have none of these tension lowering dynamics. Actually, this is not considered an option. Most would rather deal with tubeless sealants and mounting than tubular tire gluing.
(2) Make rims more massive so deformations are smaller. This is the present industry strategy. Clinchers need 100-200g each so wheels will be stable and long lived.
(3) Design rims so outward tire pressure is resisted without weight increase. Such a sophisticated solution is missing. It seems beyond industry engineers or deemed unnecessary. After all, riders voluntarily carry the extra weight around.
Here is a metal rim (to be bonded into a carbon wheel) where pressure induced sidewall deformation was unacceptable. Brake tracks do not splay with even 200psi (14bar). Design can be a solution.
The second rim deformation is reduction in total circumference. This change is not enough to affect tire fit but it definitely affects spoke tension. Unlike tubulars, clincher tires recruit the rim to be a portion of the tire hoop.
In so doing, the rim feels inward pressure. For example, many 700C road rims have internal width of 18mm a circumference at that point of about 196cm. Rim bed area is:
196cm X 1.8cm = 352.8cm^2
Inflate the tire to 90psi (6.3kgf/cm^2) and the rim feels inward force:
352.8cm^2 X 6.3kgf/cm^2 = 2223kg
This constrictive, hoop stress is inescapable with clinchers. Example, a DT RR460 rim (cross section of 0.87cm^2) sees significant stress:
Hoop stress = Pressure X Mean diameter/2(section area)
= 6.3kgf/cm^2 X 196cm/2*1.74cm^2
= 354kgf/cm^2 = 35MPa
This compressive load acts on the material’s elasticity, shrinking the hoop:
modulus of elasticity of aluminum = compression force / % change in beam length
7 X 10^10N/m^2 = 35MPa / % length change
% length change = 35MPa / 7 X 10^10N/m^2 = 0.0005
The shortening of the rim (figure a beam of 196cm length and 2223kg load) calculates to:
0.0005 X 196cm = 1mm
Empirical testing confirms hoop circumference decrease of about 1mm with 90psi inflation. Effect on spoke tension is significant.
Conclusion: Clincher tires (tubed or tubeless) load rims, causing bead hook flex and rim hoop contraction. Both encourage tension loss. Makers of rims and tires can address these dynamics with design but it looks as if they are indifferent or have little understanding of the bigger picture. To have commercially successful tires, their makers off load forces on rims, that respond by burdening the spoked structure. At this advanced stage of bike engineering (e-shifting, GPS, power measurement, hybrid materials, aerodynamics…) we should be seeing better.
Next on tension drop concerns tires themselves. Their effect on rims varies enormously. Reveal: this unique tool plays a big role in Part 2.
I hope your appreciation of wheel dynamics is expanding. Hang on for Part 2, it’s coming right up!
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