# Relationship of VAM-derived "relative w/kg" to actual w/kg?

#### jyl

I am curious about the Dr. Ferrari metric of "VAM" and the "relative watt/kg" derived from VAM.

After building a cycling power model, and plugging in some constant velocity climbs, it looks to me like the "relative w/kg" is far higher than the actual w/kg.

For example, I modeled this climb - hmm, it looks like Alpe d'Huez, doesn't it Rider 70 kg and 170 cm height, frontal area 0.411 m^2, riding on bar tops (Cd 1.15)
Clothes/shoes/helmet 1 kg, bike 7 kg, bottles/Garmin/etc 1 kg
Drivetrain efficiency 98%, no wind, no drafting
40 minute climb starting at 1000 meters altitude
Rider climbs 1066 vertical meters, covers 13.2 km, at constant 19.8 km/h
VAM is 1599 m/h and Ferrari "relative watt/kg" is 7.99
Calculated power is 412.9 watts which is 5.9 watt/kg using rider's 70 kg naked weight
7.99 is obviously very different from 5.90

Is the "relative watt/kg" derived from VAM supposed to be an estimate of the rider's actual watt/kg? Why doesn't the Ferrari formula consider rider weight?

#### Merckx index

A VAM of 1599 on an 8.1% gradient works out to 5.69 w/kg, not sure how you came up with 7.99. I guess you just divided the VAM by 2 x 100, but the correct divisor is {[2 + ( the gradient x 10)] x 100} = 281. That is how Ferrari determines w/kg, I'm not sure what "relative w/kg" means.

The actual weight is not considered because climbing speed is proportional to power/weight, regardless of the actual weight. This is not an exact relationship, it ignores bike weight, friction, air resistance, etc., but for many purposes it's close enough.

#### Alex Simmons/RST

Re: Relationship of VAM-derived "relative w/kg" to actual w/

jyl said:
I am curious about the Dr. Ferrari metric of "VAM" and the "relative watt/kg" derived from VAM.

After building a cycling power model, and plugging in some constant velocity climbs, it looks to me like the "relative w/kg" is far higher than the actual w/kg.

For example, I modeled this climb - hmm, it looks like Alpe d'Huez, doesn't it Rider 70 kg and 170 cm height, frontal area 0.411 m^2, riding on bar tops (Cd 1.15)
Clothes/shoes/helmet 1 kg, bike 7 kg, bottles/Garmin/etc 1 kg
Drivetrain efficiency 98%, no wind, no drafting
40 minute climb starting at 1000 meters altitude
Rider climbs 1066 vertical meters, covers 13.2 km, at constant 19.8 km/h
VAM is 1599 m/h and Ferrari "relative watt/kg" is 7.99
Calculated power is 412.9 watts which is 5.9 watt/kg using rider's 70 kg naked weight
7.99 is obviously very different from 5.90

Is the "relative watt/kg" derived from VAM supposed to be an estimate of the rider's actual watt/kg? Why doesn't the Ferrari formula consider rider weight?
Putting aside whether you are using correct Ferrari formula, road surface and tyres = one Crr value only, not two. Your Cd x A is probably a tad high but not a big deal depending on precision required.

#### jyl

Re: Relationship of VAM-derived "relative w/kg" to actual w/

Alex Simmons/RST said:
jyl said:
I am curious about the Dr. Ferrari metric of "VAM" and the "relative watt/kg" derived from VAM.

After building a cycling power model, and plugging in some constant velocity climbs, it looks to me like the "relative w/kg" is far higher than the actual w/kg.

For example, I modeled this climb - hmm, it looks like Alpe d'Huez, doesn't it Rider 70 kg and 170 cm height, frontal area 0.411 m^2, riding on bar tops (Cd 1.15)
Clothes/shoes/helmet 1 kg, bike 7 kg, bottles/Garmin/etc 1 kg
Drivetrain efficiency 98%, no wind, no drafting
40 minute climb starting at 1000 meters altitude
Rider climbs 1066 vertical meters, covers 13.2 km, at constant 19.8 km/h
VAM is 1599 m/h and Ferrari "relative watt/kg" is 7.99
Calculated power is 412.9 watts which is 5.9 watt/kg using rider's 70 kg naked weight
7.99 is obviously very different from 5.90

Is the "relative watt/kg" derived from VAM supposed to be an estimate of the rider's actual watt/kg? Why doesn't the Ferrari formula consider rider weight?
Putting aside whether you are using correct Ferrari formula, road surface and tyres = one Crr value only, not two. Your Cd x A is probably a tad high but not a big deal depending on precision required.

Thanks for correcting that!

#### jyl

Re:

Merckx index said:
A VAM of 1599 on an 8.1% gradient works out to 5.69 w/kg, not sure how you came up with 7.99. I guess you just divided the VAM by 2 x 100, but the correct divisor is {[2 + ( the gradient x 10)] x 100} = 281. That is how Ferrari determines w/kg, I'm not sure what "relative w/kg" means.

The actual weight is not considered because climbing speed is proportional to power/weight, regardless of the actual weight. This is not an exact relationship, it ignores bike weight, friction, air resistance, etc., but for many purposes it's close enough.

My previous response was blocked as possible spam, not sure why?

Thanks for correcting me. I was confused by Wikipedia's entry on the relative w/kg formula. Your explanation cleared it up for me!