Power Estimation vs SRM for 250 Climbs

Again apologies to Vetoo for sitting on this for so long

but

for this truly massive project Vetoo collected power meter measured

power data

and estimated power outputs using the Martin method

for 36 riders

on

a total of 250 climbs

he used best available information for weights

often confirmed by the teams

and

3 different CdAs of 0.355, 0.305, and .2625

the results of the the 0.355 CdA provided the best estimates

and

are presented above

the first figure

is measured wkg vs estimated w/kg

you can see that the linear regression is essentially

indistinguishable from the line of identity

For the stats types:

(Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -0.02232 0.07042 -0.317 0.752

x 0.99934 0.01379 72.481 <2e-16 ***

—-

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1449 on 248 degrees of freedom

Multiple R-squared: 0.9549, Adjusted R-squared: 0.9547

F-statistic: 5254 on 1 and 248 DF, p-value: < 2.2e-16)

For the non-stats types:

The fit is very good.

and the SRM value is likely to be within

+/- 1.6% of the estimate

and very likely to be within

+/- 2.7% of the estimate

(for perspective remember that SRM is accurate to within +/- 1-2%)

looking at the remaining plots

there does not seem to be a bias with power or gradient

there is a suggestion of bias with rider weight

which makes sense since a fixed CdA is used so that

the aerodynamic drag to weigh ratio is overestimated for small riders

and

underestimated for larger riders

the kernel density and QQ plots show us that the distribution of error

is reasonably normal

the final plot suggests

the accuracy of rider weight is questionable

how do I get to that conclusion ?

possible sources of systematic error

are

weight

CdA

and

Crr

of the 3

the effect of Crr will be negligible between riders

we know there is a small effect of CdA from bias we see in rider size

but not enough to explain the individual rider residuals

which leaves weight

however small errors in weight

have only a trivial effect on estimated W/kg

(if you don’t believe me try the math)

but small errors in weight

do create errors in the W/kg calculated from SRM data

large enough to explain the final figure

…

the take home points

0.35 CdA is a good estimate for the typical Pro rider

carefully done estimates when using a standard CdA

are likely to be accurate to within

+/- 1.6 % (75% confidence interval)

and

very likely to be within:

+/- 2.7% (95% confidence interval)

and

almost certainly within

+/- 3.6% (99% confidence interval)

when attempting to “calibrate” individual estimates against SRM data

having an accurate weight is absolutely critical

or better yet

SRM data from several riders is considered