For anyone interested: Someone replied on the weight weenies forum. Basically Latex tubes will always be faster unless doing a massive hill climb with average gradients above 15%.
This isn’t difficult to calculate, if you have the data. Inner tubes don’t affect power production or aerodynamics, they just affect weight and rolling resistance.
Drag due to mass on a slope is: Fgravity = (M + m) x g x sine(A)
Rolling resistance drag is: Frolling = Crr x m x g x cosine(A)
where:
M = entire mass of bike/rider minus mass of inner tubes
m = mass of inner tubes
g = acceleration of gravity
A = angle of slope
Crr = coefficient of rolling resistance.The angle where the extra rolling resistance of TPU tubes balances out the lower rolling resistance of latex can be found by setting the gravity and rolling resistances of TPU and latex tubes equal:
Fgravity,ltx + Frolling,ltx = Fgravity,tpu + Frolling,tpu
(M + m,ltx) x g x sine(A) + CXrr,ltx x (M + m,ltx) x g x cosine(A) = (M + m,tpu) x g x sine(A) + Crr,tpu x (M+m,tpu) x m x g x cosine(A)
Rearranging to solve for angle A, leaves this formula
A = arctangent( ( (Crr,tpu - Crr,ltx) * M + Crr,tpu * m,tpu - Crr,ltx * m,ltx ) / ( m,ltx - m,tpu ) )
The Aerocoach web page has some data on inner tube mass and rolling resistance (https://www.aero-coach.co.uk/inner-tube … resistance):
Vittoria latex tubes: m,latex = 72 grams, Crr,latex = 0.002612
Tubilito S TPU tubes: m,tpu = 22 grams, Crr,tpu = 0.002931Assuming a total bike/rider (minue inner tubes) mass of 75 kg (75,000 g), the slope at which the lower weight of TPU tubes overcomes their higher rolling resistance is 25.4 degrees, or a grade of 48%. Which means on a practical basis, latex tubes will always be faster, even on steep slopes.
Hi Mark, this is great, but your specific calculation of 25.4 degrees appears to be for a unicycle. If the rider+cycle mass is shared by two wheels then things look quite a lot better for TPU.
Oops! Good catch! You’re right, I only added the weight of a single tube. When considering the weight of two tubes, than the “critical” slope for the 75 kg bike/rider is 23.6% (13.3 degrees), and for the 50 kg bike/rider the critical slope is 15.7% (8.9 degrees). So there are a few, rare, real world cases where the slope is steep enough for TPU tubes to have a performance advantage, but for most riders most of the time TPU tubes will still be a net performance disadvantage, compared to latex.