Calculating likely hill climb times

neeb

What would the best formula be for calculating the likely time taken for a climb, given average watts per kilo (including bike weight), average gradient and distance? Obviously other factors will come into play, but I guess you should be able to get a pretty good estimate based on these numbers, perhaps factoring in a constant to deal with air resistance and other stuff? Is there a calculator online anywhere?

I feel I should be able to work this out myself... I blame the nice bottle of Westmalle Tripel I've just had...

Alex_Simmons/RST

analyticcycling.com
is the best online calculator

will need total mass, estimates of air density, rolling resistance and aerodynamic drag.

Steeper the climb, the greater the proportion of energy output goes to overcoming gravity.

not sure if it includes a wind factor.

I built my own. you just need to solve this equation for speed:
http://s220.photobucket.com/albums/dd22 ... ling-2.png

neeb

Thanks, although I can't get the calculator at analyticycling to work very well, I must be missing something in one or more of the parameters.

If I go to this page:
http://analyticcycling.com/DiffEqMotion ... _Page.html
..and enter 70kg for bike + rider, 0.057 for slope, 17100m for distance (this is Mt. Diablo South Gate in California) 260W for power (using the average power option) and leave all of the other variables at their defaults (what is "time at end", default 75s? This is what I'm trying to calculate and if it's set to zero it doesn't seem to work), I get 4442.2s for rider time at 17100m, i.e. about 74 minutes. However, when I go to this page:
http://analyticcycling.com/ForcesSpeed_Page.html
..and again enter 260W, 70kg and 0.057 slope, it gives me 5.57m/s, which would be about 51 minutes over 17100m.

My actual times on this run on two occasions last summer were 59m42s and just over 61m. My average watts estimate could be out, as it's based on what my Tacx Fortius tells me I put out over an hour of climbing and it's not known to be very accurate (I don't have any other way to measure power).

What I'd like to do is estimate times for other real climbs I haven't done based on my times for climbs I have done. It would also be useful if I could get an estimate of average power over 1 hour based on my time for a real climb that might be more accurate than the Fortius figures.

mrushton

It's meant to be fun not a Ph.D from MIT. You could try www.cyclefit.co.uk and read about Garth Fox's presentation or go to www.garthfox.com
He is pretty clued up re power data

Alex_Simmons/RST

mrushton wrote:

It's meant to be fun not a Ph.D from MIT. He is pretty clued up re power data

He asked for the best. On line that is analyticcycling.com

Alex_Simmons/RST

neeb wrote:

Thanks, although I can't get the calculator at analyticycling to work very well, I must be missing something in one or more of the parameters.

I think the Tacx numbers are to be taken with a large grain of salt.

1. Use the static forces tool. Click on Toolkit button.

2. choose to solve for power, given speed
Use a known climb (a climb you have done where you know gradient and speed). That will give you a power output requirement.

3. then use static forces, speed for given power option
Use that previously calculated power up another known climb gradient to see the speed you would do (assuming same power and other assumptions)

neeb

Thanks again.

Really interesting. Firstly, if the figures are correct then my average wattage over an hour is quite a bit less than I thought, which is a bit depressing. On the other hand, it suggests that if I can go up Mt. Diablo in just under an hour (17.38km from where I started, 5.7% av. gradient), I should have a chance of fulfilling an ambition of doing Alpe d'Huez in under an hour (13.2km, 8.1%).

However this data is suggesting that you only need about 3.5 w/kg (not including bike) to do both of these climbs in 1 hour, whereas I got the impression from a number of other sources that it was nearer 4.

Alex_Simmons/RST

neeb wrote:

Thanks again.

Really interesting. Firstly, if the figures are correct then my average wattage over an hour is quite a bit less than I thought, which is a bit depressing. On the other hand, it suggests that if I can go up Mt. Diablo in just under an hour (17.38km from where I started, 5.7% av. gradient), I should have a chance of fulfilling an ambition of doing Alpe d'Huez in under an hour (13.2km, 8.1%).

However this data is suggesting that you only need about 3.5 w/kg (not including bike) to do both of these climbs in 1 hour, whereas I got the impression from a number of other sources that it was nearer 4.

Here's some info on Alpe d'Huez:
http://alex-cycle.blogspot.com/2011/07/ ... rtals.html

Also, make sure you are using correct inputs.
Weight is the mass of bike + rider + all your gear

Rolling resistance is likely to be closer to 0.005.
0.004 is for very good road and very fast tyres. (AC.com's rolling resistance quoted guidelines are a bit low)

Cd can set that to 1 and simply input a CdA value in the Frontal Area input (those two are simply multiplied together in the calculations).

Assuming climbing on hoods or tops, then probably 0.32-0.38m^2 I'd guesstimate (more if wearing a flappy rain jersey), although on steeper climbs the result isn't overly sensitive to the CdA estimate.

Air density you can adjust for but like CdA, it shouldn't be overly sensitive to that on steep climbs.

neeb

Yup, I'm getting there! Tacx Fortius was telling me I was putting out over 4 w/kg over 1 hour, doubtless an overestimate. Initially when I put the figures into the AC calculator based on my Mt. Diablo effort it was giving about 3.5 w/kg, but I'd been using the default values for Cd, CdA and rolling resistance, and although I'd factored in the weight of the bike I hadn't included the gear. Turns out it's not insignificant - over 2 kg! And that's not including the 750ml or so of water I consumed on the way up (let's skip the physics, biology and calculus required to factor that in... )



With Cd at 1, CdA at 0.34, rolling resistance at 0.005 and the correct total weight, I'm now getting about 3.73 w/kg (for body weight alone), which puts me very near what your chart tells me I would need to do the Alpe d'Huez in an hour. It just won't be quite as easy as on the Fortius...

Alex_Simmons/RST

neeb wrote:

With Cd at 1, CdA at 0.34, rolling resistance at 0.005 and the correct total weight, I'm now getting about 3.73 w/kg (for body weight alone), which puts me very near what your chart tells me I would need to do the Alpe d'Huez in an hour. It just won't be quite as easy as on the Fortius...

No turbo style electro-braked trainer has the ability to really simulate the loads of such steep sustained climbs (more than about 7-8%). They simply don't work that well at low wheel speeds despite their claims and will usually incorrectly report power and/or allow an unrealistic speed as a result.

No matter, use the trainer to help improve power output and you'll still climb better.

Eyorerox

If you have a Garmin you could log your Diablo climb into Strava and they will give you an estimate of your wattage
in my experience not very encouraging numbers!
http://www.strava.com/

neeb

I think I need to hire a proper power meter for a week sometime and get a handle on approximately calibrating the Fortius. Accurate or not, it's remarkably consistent over a given route if I'm careful with the tyre & roller pressures.

simon_e

neeb wrote:

I think I need to hire a proper power meter for a week sometime and get a handle on approximately calibrating the Fortius. Accurate or not, it's remarkably consistent over a given route if I'm careful with the tyre & roller pressures.

Nah, just find some hills and ride up them, timing yourself with a stopwatch.

Saving a few grammes by buying lighter shoes or helmet won't make any difference either.

neeb

Simon E wrote:

Nah, just find some hills and ride up them, timing yourself with a stopwatch.

I'd love to! Stuck in Southern Finland for most of the winter unfortunately. No hills to speak of and it's bloody cold and dark..

Might be back in Berkeley early next year though. No shortage of hills there... In fact the problem there is you can't so much as warm up before the first major climb.