# The effect of hills on average speed?



## huggy (21 May 2013)

Can you calculate the effect of hills on average speed.

When walking you can use Naismiths rule, to give you a target or estimation how long it will take.

So this evening I did this average 13mph over 18 miles with 1100 ft of up and down (it was a loop).
http://ridewithgps.com/trips/1339967

Can we esimate what my average would be on a flatter course, not many flat roads to actually do it round here.


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## Nebulous (22 May 2013)

Hi - I've no idea if there is a rule, but I have several loops I use depending on time available / tiredness etc. I've built up a fair bit of data on what speed / time I can do them in and there is quite a bit of variability, which is more wind dependent than anything else.

Over 30-50 miles my flattest routes have about 35 feet of climb per mile. The highest I usually get is high 50s which is just under where you are at (61 feet of climb per mile) and that knocks between 1 and 1.5 mph off my average.


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## redcard (22 May 2013)

About the same?


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## GrasB (22 May 2013)

huggy said:


> Can you calculate the effect of hills on average speed.
> 
> When walking you can use Naismiths rule, to give you a target or estimation how long it will take.
> 
> ...


To get an idea of your ride time on a hill climb you need to do is get a good idea of your nominal altitude gain (VAM) an hour, your flat road still air cruising speed (V), then also know your total distance (D) & total elevation gain on the ride (EG).
D / V + EG / VAM
For arguments sake say you have 500m/h VAM & 25km/h V. You're doing a 40km ride with 200m climbing
D / V = 40/25 = 1.6h
EG / VAM = 200/500 = 0.4h
1.6 + 0.4 = 2h
So 20km/h (or 12.5mph).

This will always over estimate your time if you're doing a ride that include down hill sections as it is extremely hard to estimate your down hill speed. Put it this way, descend like a demon & be sprinting out of the corners to get up to Vmax ASAP on the descent (5% will get you to 25mph fairly easily on the hoods a road bike) will have a huge impact on your average speed rather than gently feathering the brakes keeping the speeds under 25mph.


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## uclown2002 (22 May 2013)

How many climbing feet per mile would be considered flat, hilly etc?

http://app.strava.com/activities/55473630

107 feet per mile; seems rather common where I live. My 23 mile commute still has 85 climbing feet per mile and that feels relatively flat compared to most of my rides.


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## GrasB (22 May 2013)

my guide is on a longish circular route:
Flat = 0-5m/km
Rolling = 5-10m/km
mildly hilly = 10-15m/km
hilly = 15-20m/km
very hilly = 20-30m/km
insane >30m/km


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## Nigelnaturist (22 May 2013)

uclown2002 said:


> How many climbing feet per mile would be considered flat, hilly etc?
> 
> http://app.strava.com/activities/55473630
> 
> 107 feet per mile; seems rather common where I live. My 23 mile commute still has 85 climbing feet per mile and that feels relatively flat compared to most of my rides.


Is that over the course of the ride. I just can't get anywhere near that normally including rides like this.


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## Globalti (22 May 2013)

GrasB said:


> my guide is on a longish circular route:
> Flat = 0-5m/km
> Rolling = 5-10m/km
> mildly hilly = 10-15m/km
> ...


 
Wow! Up here in Lancashire 25 metres of climb in 1 km is mild! A relatively gentle climb that most cyclists have to do is Bailey Bank, from the river Hodder to a place called Walker Fold just north of Longridge Fell; it climbs 109m in 3 km, so just over 36 m per km. Further along the same road you've got Jeffrey Hill, which climbs 135m in 1.35 km, so 100 m per km and is my more direct route home if I'm feeling strong enough late in a long ride.


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## uclown2002 (22 May 2013)

Nigelnaturist said:


> Is that over the course of the ride. I just can't get anywhere near that normally including rides like this.


Yes, that particular route I linked to was 46.5 miles with an elevation gain of 4974 feet; so if my sums are right that is 107 feet per mile. Three Cat 4 climbs in there, but hard to avoid the hills near home.


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## HLaB (22 May 2013)

GrasB said:


> my guide is on a longish circular route:
> Flat = 0-5m/km
> Rolling = 5-10m/km
> mildly hilly = 10-15m/km
> ...


I'm surprised my commute this morning actually scrape into the 'Rolling' territory I,ve have to go out and seek hills bumps on the steel fixie.


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## jowwy (22 May 2013)

GrasB said:


> my guide is on a longish circular route:
> Flat = 0-5m/km
> Rolling = 5-10m/km
> mildly hilly = 10-15m/km
> ...


 my commute home is 100ft/mile - so whats that on your rough guide??


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## Nigelnaturist (22 May 2013)

jowwy said:


> my commute home is 100ft/mile - so whats that on your rough guide??


about 19m/Km


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## Rob3rt (22 May 2013)

jowwy said:


> my commute home is 100ft/mile - so whats that on your rough guide??


 
Convert ft to meter and mile to km, do the division, then look at his post?


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## GrasB (22 May 2013)

GrasB said:


> my guide is on a *longish circular* route:
> Flat = 0-5m/km
> Rolling = 5-10m/km
> mildly hilly = 10-15m/km
> ...


 


Globalti said:


> Wow! Up here in Lancashire 25 metres of climb in 1 km is mild! A relatively gentle climb that most cyclists have to do is Bailey Bank, from the river Hodder to a place called Walker Fold just north of Longridge Fell; it climbs 109m in 3 km, so just over 36 m per km. Further along the same road you've got Jeffrey Hill, which climbs 135m in 1.35 km, so 100 m per km and is my more direct route home if I'm feeling strong enough late in a long ride.


Go back & think about this again after re-reading my post, paying attention to the bold bit.
Hint: in the 2010 TdF out & back of the 25 categorised climbs would give you 8 which did not make it to >30m/km. One of those was an HC category climb.


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## jowwy (22 May 2013)

Nigelnaturist said:


> about 19m/Km


so its hilly then lol

which makes the sportive i did onthe weekend hilly too......and very nearly in the very hilly category, no wonder i was tired at the end


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## BSRU (22 May 2013)

"Mildly hilly" accurately sums up my commute, generally between 10 to 15 m per km.
Although if I exclude the start and finish in the town which is flat it would push the out of town part to nearer "hilly".


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## GrasB (22 May 2013)

Opps, just realised the last band is 20-30 not 20-25


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## Nigelnaturist (22 May 2013)

jowwy said:


> so its hilly then lol
> 
> which makes the sportive i did onthe weekend hilly too......and very nearly in the very hilly category, no wonder i was tired at the end


But as GrasB points out over a longish route, I did 42.2miles yesterday and got 62.67ft/mile or 67.88Km with 11.62m/Km and that included a Cat3. it was the ride to it and home that brought it down.


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## Globalti (22 May 2013)

Oh, so it's the climb over the entire ride then?


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## ColinJ (22 May 2013)

Globalti said:


> Oh, so it's the climb over the entire ride then?


Yes!

The local Season of Mists audax is what I would call extremely hilly ... 







... about 2,500 m of climbing in its 100 km, which fits in pretty nicely with GrasB's ratings.


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## jowwy (22 May 2013)

Nigelnaturist said:


> But as GrasB points out over a longish route, I did 42.2miles yesterday and got 62.67ft/mile or 67.88Km with 11.62m/Km and that included a Cat3. it was the ride to it and home that brought it down.


it was 4950ft of climbing over 49.1 miles which equates to 18.99m/km


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## Nigelnaturist (22 May 2013)

jowwy said:


> it was 4950ft of climbing over 49.1 miles which equates to 18.99m/km


Be about right then as mine yesterday was 61.36ft/mile (11.62m?Km) and 2588ft over 42.2 miles.


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## PpPete (24 May 2013)

GrasB said:


> To get an idea of your ride time on a hill climb you need to do is get a good idea of your nominal altitude gain (VAM) an hour, your flat road still air cruising speed (V), then also know your total distance (D) & total elevation gain on the ride (EG).
> D / V + EG / VAM
> For arguments sake say you have 500m/h VAM & 25km/h V. You're doing a 40km ride with 200m climbing
> D / V = 40/25 = 1.6h
> ...


 
I've always reckoned that the effect of downhills on the average speed comes close to balancing out stretches where one is held up at junctions, deceleration/acceleration time being quite significant.
I've been tinkering with spreadsheets to try and estimate timings over long audax rides but the whole thing goes a bit a pear-shaped when you start working with VAM numbers.
Looking at my stats from the recent BCM 600, my VAM (from Strava) on the Saturday was averaging around 480, on the Sunday around 425 (pretty sh!t, I know) but working things backwards on my spreadsheet (which does GrasB's calculation for me) so that it corresponds with the times I actually took on each leg.... my V on the Saturday would have to be a highly improbable 48km/h and on the Sunday, an only slightly more plausible 36km/h. 
I know there some cracking descents, the one on the A470 after Cross Foxes down to Dinas Mawddwy for example, provides a couple of km at speeds above 60km/h but the effect on the overall average is pretty negligible:
My average speed from the top of that particular descent to the control at Aberhafesp (50 km) : 22km/h
from the bottom of the descent to the control: average 21 km/h


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## redcard (24 May 2013)

PpPete said:


> I've always reckoned that the effect of downhills on the average speed comes close to balancing out stretches where one is held up at junctions, deceleration/acceleration time being quite significant.
> I've been tinkering with spreadsheets to try and estimate timings over long audax rides but the whole thing goes a bit a pear-shaped when you start working with VAM numbers.
> Looking at my stats from the recent BCM 600, my VAM (from Strava) on the Saturday was averaging around 480, on the Sunday around 425 (pretty sh!t, I know) but working things backwards on my spreadsheet (which does GrasB's calculation for me) so that it corresponds with the times I actually took on each leg.... my V on the Saturday would have to be a highly improbable 48km/h and on the Sunday, an only slightly more plausible 36km/h.
> I know there some cracking descents, the one on the A470 after Cross Foxes down to Dinas Mawddwy for example, provides a couple of km at speeds above 60km/h but the effect on the overall average is pretty negligible:
> ...



See post 3


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## PpPete (24 May 2013)

redcard said:


> See post 3


 
so you saying that on a flat course I couldn't ride at pro peleton speeds ?


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## GrasB (24 May 2013)

PpPete said:


> I've always reckoned that the effect of downhills on the average speed comes close to balancing out stretches where one is held up at junctions, deceleration/acceleration time being quite significant.
> I've been tinkering with spreadsheets to try and estimate timings over long audax rides but the whole thing goes a bit a pear-shaped when you start working with VAM numbers.
> Looking at my stats from the recent BCM 600, my VAM (from Strava) on the Saturday was averaging around 480, on the Sunday around 425 (pretty sh!t, I know) but working things backwards on my spreadsheet (which does GrasB's calculation for me) so that it corresponds with the times I actually took on each leg.... my V on the Saturday would have to be a highly improbable 48km/h and on the Sunday, an only slightly more plausible 36km/h.
> I know there some cracking descents, the one on the A470 after Cross Foxes down to Dinas Mawddwy for example, provides a couple of km at speeds above 60km/h but the effect on the overall average is pretty negligible:
> ...


I'm probably using a slightly odd definition of VAM. In that I think of VAM the fastest I could climb up a vertical face on my bike in a vacuum. If that is assumed it works.


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## PpPete (24 May 2013)

GrasB said:


> I'm probably using a slightly odd definition of VAM. In that I think of VAM the fastest I could climb up a vertical face on my bike in a vacuum. If that is assumed it works.


That's the way I thought of it too..... and so was hoping to use VAM data (with a bit of arithmetic) in a similar way to Naismith's formula.
But looking more closely at the Strava VAMs, they seem to divide the ascent mtrs by the total time (which of course includes both horizontal and vertical components).
Some sort of fudgeration factor would appear to be needed. Based on a very limited dataset I think dividing by something like 1.67 will convert Strava VAMs to what you and I think of as "true" VAMs.


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## GrasB (24 May 2013)

VAM normally is taken to be climbing ability up a hill of around 20-25%. Your VAM increases as the road speed decreases (or as the hill gets steeper, but it's not the steepness of the hill that's key, it's the reduction of aerodynamic drag).


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