Random Friday Question (Climbing)

g0g

Had this in my head the other day and was wondering if there's a known answer. For the sake of this questuion ignore the type of surface and the weather conditions etc. Assume a normal day, dry road etc and also assuming a standing start.

Is there an "ideal" incline to climb say 100m as quickly as possible? I hope the question is easy to understand. i.e. would it be quicker to climb at a painful 20% angle for the 100m (short distance slowly) or would a very light slope be much much quicker to do (longer distance quickly)? I realise this is starting to sound like a Top Gear race or something like that....

The follow-on question then would be as to whether the "ideal" slope would change based on how much you want to climb.

smacl

I would guess gearing, weight, and fitness are variables you couldn't ignore in this question, so there isn't a single good answer. Basically it's going to come down to effort over time, e.g. less effort over a longer time or more effort over a shorter one. Sounds like a job for power meter guy.

Actually thinking about it, I'd be much more fearful of the short ramps like the wall than the longer drags like shay elliot. Must try to drop a couple of pounds more before the Orwell gig.

g0g

smacl wrote: »

I would guess gearing, weight, and fitness are variables you couldn't ignore in this question, so there isn't a single good answer. Basically it's going to come down to effort over time, e.g. less effort over a longer time or more effort over a shorter one. Sounds like a job for power meter guy.

Actually thinking about it, I'd be much more fearful of the short ramps like the wall than the longer drags like shay elliot. Must try to drop a couple of pounds more before the Orwell gig.

Yeah I realise there's fitness too, so maybe assume equal level of fitness between the two cyclists, one of who is good at flat sprints and one who flies up hills.

Dr.Millah

I would imagine it would depend on a persons style, a serious masher might have a better time on the big incline as cadence would likely be low.

You may also get the benefit of going mad for the first 50 meters before your HR climbs up and you start puffing air. If you get that far you only have another 50m to go so you could slog it out at close to max output.

DirkVoodoo

Are you looking at this from an energy consumption point of view, i.e. is there a set amount of energy "available" to each cyclist in these scenarios, and which would be the "easiest" way to burn that up?

Zen0

The ideal distance is the one which uses the least energy. That is a vertical climb. Unfortunately most of us don't have the power output to achieve this (escape velocity). Possibly Ryan Sherlock does, judging by his Strava results.

smacl

I think the slope you pick is going to be based on what part of your climbing you want to improve. For short steep slopes, you're going to be expending much more energy for a shorter duration, so that's what you practice. For long climbs, you'll expend more energy overall but over a longer duration.

Given a choice of two hills on your route, if you get into the habit of choosing the one you find more difficult, it ought to become easier quite quickly. Note that I don't practice what I preach here. I still tend to take Cruagh - Johnnie Foxes as my lunch time spin, whereas up and down Kilmashougue could be better use of my time. The devils elbow as a last kicker after a long spin is another great one to test the mental and physical endurance.

g0g

Thanks for the thoughts. I'm just taking it on a simple level. If I said I want to set the world record for time taken from standing still to reach a point 100m while cycling a bike on a road, is there an ideal slope for that road?

This might be answering my own question, but does Strava have a stat showing minutes per vertical metre against climbs? That would give me my answer right away surely! (although I'd have to compare 100m climbs)

g0g

smacl wrote: »

I think the slope you pick is going to be based on what part of your climbing you want to improve. For short steep slopes, you're going to be expending much more energy for a shorter duration, so that's what you practice. For long climbs, you'll expend more energy overall but over a longer duration.

Given a choice of two hills on your route, if you get into the habit of choosing the one you find more difficult, it ought to become easier quite quickly. Note that I don't practice what I preach here. I still tend to take Cruagh - Johnnie Foxes as my lunch time spin, whereas up and down Kilmashougue could be better use of my time. The devils elbow as a last kicker after a long spin is another great one to test the mental and physical endurance.

Thanks for the thoughts although FYI it's nothig to do with (lack of!) climbing skills. I'm just wondering which would be faster time-wise.

smacl

g0g wrote: »

Thanks for the thoughts although FYI it's nothig to do with (lack of!) climbing skills. I'm just wondering which would be faster time-wise.

For faster, I'd guess its more about putting out very large amounts of energy in a short time, which suggests repeats on very steep slopes. Shallower gradients and/or slower speeds for long periods will build endurance rather than strength.

Mr. Grieves

g0g wrote: »

This might be answering my own question, but does Strava have a stat showing minutes per vertical metre against climbs? That would give me my answer right away surely! (although I'd have to compare 100m climbs)

Yes, look at the VAM for the same person for different climbs. Per Strava:

"VAM measures your Vertical Ascent in Meters/hour – it measures how quickly you are traveling upward. VAM is useful for comparing your effort on different hills and segments, and is used by both cyclists and runners. To get a high VAM score, grades between 6-10% generally present the best opportunity to ascend quickly, as they are steep enough to avoid wind, and gradual enough to allow unrestricted motion."

C3PO

Is Lumen away? I'd have expected a detailed answer and technical diagram by now!

ROK ON

g0g wrote: »

Thanks for the thoughts. I'm just taking it on a simple level. If I said I want to set the world record for time taken from standing still to reach a point 100m while cycling a bike on a road, is there an ideal slope for that road?

This might be answering my own question, but does Strava have a stat showing minutes per vertical metre against climbs? That would give me my answer right away surely! (although I'd have to compare 100m climbs)

As previous poster mentioned VAM is the unit of measurement. One proviso - I have found that it is only really useful on like for like measurement.

My VAM on long shallow climbs is about 23% below my VAM for steep climbs. Why, I think on very steep climbs there is a minimum speed necessary to simply stay upright - thus I push very hard to simply stay upright. On shallow climbs this doesnt isnt such a factor.

So I think that may get to your answer, in that I would cover 100m of ascent on a steep climb faster than I would for a shallow climb.
Because of that, I only ever compare my VAM on the same climb - I dont compare my VAM on one climb to another. According to wiki, a 1% point increase in gradient increases VAM by 50m.
http://en.wikipedia.org/wiki/Velocity_Ascended,_Metres_per_hour

Lumen

ROK ON wrote: »

My VAM on long shallow climbs is about 23% below my VAM for steep climbs. Why, I think on very steep climbs there is a minimum speed necessary to simply stay upright - thus I push very hard to simply stay upright. On shallow climbs this doesnt isnt such a factor.

Air resistance is greater on shallow climbs.

Lumen

The solution for ultimate VAM is to connect your cranks to a vertical pulley system, Tarzan-style.

Although I think it was Cheetah who pulled Tarzan up to his treehouse, and I don't know much about bikefit for chimpanzees, they presumably need a very compact frameset. Anyway, I'm not sure why he was called Cheetah, I think he fought off a cheetah or something.

smacl

Lumen wrote: »

Air resistance is greater on shallow climbs.

You're also expending time and effort travelling the horizontal component of the journey, unless of course you're taking the Tarzan route again. Also, Cheetah is cheating, as he's using his arms as well as legs for the ascent, and his bike weighs a very tidy 0g. If you're only considering the upward vertical component, bikes are probably a sub-optimal mode of transport, coming back down on the other hand...

el tel

I would say yes there is an ideal gradient for a particular individual to make 100 vertical ascent in minimum time. The only sane way to find it would be empirically. Like on a variable incline treadmill timed over the distance per particular degree/min/sec of gradient. By the time youd tried all the inclines youd be so much fitter that you were t the start the earlier results would be superseded. or maybe not.

If you know how quickly you can ride the following distances at the following constant gradients, then you will be able to close in on the answer

Distance (m) Gradient (Deg)

5729.87 1
2865.37 2
1910.73 3
1433.56 4
1147.37 5
956.68 6
820.55 7
718.53 8
639.25 9
575.88 10
524.08 11
480.97 12
444.54 13
413.36 14
386.37 15
362.80 16
342.03 17
323.61 18
307.16 19
292.38 20
279.04 21
266.95 22
255.93 23
245.86 24
236.62 25
228.12 26
220.27 27
213.01 28
206.27 29

Getting into SpiderPig territory…

200.00 30
194.16 31
188.71 32
183.61 33
178.83 34
174.34 35
170.13 36
166.16 37
162.43 38
158.90 39
155.57 40
152.43 41
149.45 42
146.63 43
143.96 44
141.42 45
139.02 46
136.73 47
134.56 48
132.50 49
130.54 50
128.68 51
126.90 52
125.21 53
123.61 54
122.08 55
120.62 56
119.24 57
117.92 58
116.66 59
115.47 60
114.34 61
113.26 62
112.23 63
111.26 64
110.34 65
109.46 66
108.64 67
107.85 68
107.11 69
106.42 70
105.76 71
105.15 72
104.57 73
104.03 74
103.53 75
103.06 76
102.63 77
102.23 78
101.87 79
101.54 80
101.25 81
100.98 82
100.75 83
100.55 84
100.38 85
100.24 86
100.14 87
100.06 88
100.02 89
100.00 90

Rofo

I'm not touching this one. As far as I know, gravity doesn't exist on flat roads

sled driver

Rofo wrote: »

I'm not touching this one. As far as I know, gravity doesn't exist on flat roads

Ya, gravity sucks, man !!!

Beasty

You can play about with the bike calculator, if you put out, say, 300w over a 100m climb

5% slope (2km distance) - 5.84mins

10% (1km) - 4.91mins

20% (500m) - 4.66mins(the improvement at higher gradients tails off rapidly beyond 20%)

Now that assumes you can put out the same power on the same slope. I personally find it easier to put out higher power on steeper slopes (when I am out of the saddle), which suggests steeper but shorter is "easiest". That makes sense if you think about it. If the slope was 1% you would need to travel 10km to ascend 100m. To do that in 5 minutes would need a speed of 120kph. Clearly the air resistance would prevent anything approaching such a speed

smacl

el tel wrote: »

Distance (m) Gradient (Deg)

100.00 90

[Pedantic b'stard mode]The horizontal distance at 90 degrees is 0m. 100m horizontal to 100m vertical is a gradient of 1:1 or 45%.[/Pedantic b'stard mode]

el tel

smacl wrote: »

[Pedantic b'stard mode]The horizontal distance at 90 degrees is 0m. 100m horizontal to 100m vertical is a gradient of 1:1 or 45%.[/Pedantic b'stard mode]

You are not wrong but the distances listed are not horizontal distances. They are distance to travel.

Rofo

g0g wrote: »

Had this in my head the other day and was wondering if there's a known answer. For the sake of this questuion ignore the type of surface and the weather conditions etc. Assume a normal day, dry road etc and also assuming a standing start.

Is there an "ideal" incline to climb say 100m as quickly as possible? I hope the question is easy to understand. i.e. would it be quicker to climb at a painful 20% angle for the 100m (short distance slowly) or would a very light slope be much much quicker to do (longer distance quickly)? I realise this is starting to sound like a Top Gear race or something like that....

The follow-on question then would be as to whether the "ideal" slope would change based on how much you want to climb.

Having just watched yesterday's Giro del Tretino mountain-finish stage with a couple of beers, I've arrived at what is definitely the right the answer to this: It all depends on two things - your power:weight ratio and overall weight.

Leaving aside the minimal increases in rolling resistance and inertial resistance that a heavier rider is subject to for a moment - let's imagine two riders. One with slightly better power:weight ratio, the other being 10kg lighter. Set them off and point the road up by a degree every 100m, the rider with better power:weight ratio will do better at first but at some tipping point that I haven't a clue how to work out, it will become tougher for the heavier stronger rider as the incline becomes steeper and the lighter rider will do better. (I'm thinking of how Jose Rujano and Pozzavivo took over yesterday when they hit 20 degree stuff)

...or maybe that's b0llock5 :-). Maybe it's not realistic to think of humans in physics terms and there are other variables that come into play that have a greater effect: The psychological effect of seeing a ridiculous 'wall' ahead of you; the almost panic effect that a sustained output of near peak power has on your body; or just imagining that the smaller climber has the advantage.

Keep_Her_Lit

All other things being equal, the rider with the better power to weight ratio will climb faster. The whole point of this metric is that it normalises power output with respect to weight. In other words, it isn't absolute (or overall) weight that matters but the number of Watts available to propel each kg of weight. Ultimately it does come down to physics.

Moreover, the steeper the gradient, the better the measured performance will correlate to the power to weight ratio.

The situation you describe would be atypical, I think, i.e. where the heavier rider has the superior power to weight ratio. The reason the best climbers have the classical "mountain goat" physiques is because that's the make up which delivers the highest power to weight ratio. All muscle and sinew, no fat and proportionately large heart and lungs.

The same applies in other sports. Look at the weights that Olympic Weightlifters shift in the lower weight classes. As a proportion of body weight, they are significantly greater than those achieved by the heavyweights. That is, the lighter the class, the higher the power to weight ratio.

This seems to hold true throughout the animal kingdom. A chimpanzee is a much more accomplished gymnast than a silverback gorilla, even though the latter has a much greater maximum power output. The ant dwarfs both of them and is enormously powerful for its size.

I want to emphasize here that I am not in any way attempting to equate good climbers with either chimpanzees or ants.

Rofo

Keep_Her_Lit wrote: »

All other things being equal, the rider with the better power to weight ratio will climb faster. The whole point of this metric is that it normalises power output with respect to weight. In other words, it isn't absolute (or overall) weight that matters but the number of Watts available to propel each kg of weight. Ultimately it does come down to physics.

Moreover, the steeper the gradient, the better the measured performance will correlate to the power to weight ratio.

The situation you describe would be atypical, I think, i.e. where the heavier rider has the superior power to weight ratio. The reason the best climbers have the classical "mountain goat" physiques is because that's the make up which delivers the highest power to weight ratio. All muscle and sinew, no fat and proportionately large heart and lungs.

The same applies in other sports. Look at the weights that Olympic Weightlifters shift in the lower weight classes. As a proportion of body weight, they are significantly greater than those achieved by the heavyweights. That is, the lighter the class, the higher the power to weight ratio.

This seems to hold true throughout the animal kingdom. A chimpanzee is a much more accomplished gymnast than a silverback gorilla, even though the latter has a much greater maximum power output. The ant dwarfs both of them and is enormously powerful for its size.

Ok I can follow you on the theory of 'power:weight ratio normalises power output with respect to weight' thing. Here's where I lose it: Why don't those same little guys do as well on the flat?

What are we missing here? There must be other factors that we are leaving out! Does it eventually matter that the 'power' factor of a heavier rider with the same power:weight ratio as a lighter rider does actually require more power, hence they require more fuel that their systems find more challenging to consume, process and/or deliver?

Don't forget the little guy's bike weighs the same as the big guy's - they're not in proportion! Advantage big guys surely!!

What is it about going uphill that hands the advantage to the little guy with good power:weight ratio?

Keep_Her_Lit

On the flat, at a steady racing speed, nearly all of the power dissipated is being used to overcome aerodynamic drag. That is, wind resistance is the dominant factor, while the influence of gravity is negligble (not zero, since rolling resistance increases with weight).

So it could be crudely stated that on the flat, what matters is not the power to weight ratio but the power to frontal area ratio*. And this is where the advantage goes to the larger riders. The reason? The volume of a rider's body scales with his/her weight. But the frontal area doesn't.

Take the example of a 60kg rider vs. a 90kg rider. Assuming a body density of 1kg/litre (the same as water), the volumes of their bodies will be 60 and 90 litres respectively. That is, if they each do the Eureka trick and jump into a bath brimful of water, one will displace 60 litres of water and the other will displace 90 litres.

For simplicity, let's use the formulae for the volume of a sphere and the area of a circle to compare the change in volume with the change in frontal area. If the 90kg rider is squashed into a 90 litre sphere, he will have a radius of 27.8cm and a frontal area of 2,428cm2. Likewise, if the 60kg rider is squashed into a 60 litre sphere, he will have a radius of 24.3cm and a frontal area of 1,853cm2.

Now look at the ratios of the frontal areas: 2,428cm2/1,853cm2 = 1.31

So, we can conclude that if our competitive cyclists are sphere shaped, a 50% increase in rider weight will result in a 31% increase in frontal area. More generally, if the weight is scaled by X (X = 1.5 in this example), the frontal area is scaled by X^(2/3) [X raised to the power of 2/3]

Fair enough, not many competitive cyclists are sphere shaped. However, the general principle will still hold and it is left as an exercise to the reader to establish realistic figures for human body shapes.

Now let's rig the example with some carefully selected power to weight ratios which ensure that the heavier rider turns out to be faster on the flat but slower on the climbs

OK, we're going to choose 20 minute power to weight ratios of 6.0W/kg for the mountain maestro and 5.5W/kg for the sprint star. So the whippet can hold 360W for 20 minutes, while the beefcake can belt out 495W over the same interval.

These power to weight ratios immediately suggest that the lighter guy is going to be quicker on the climbs. But, as you correctly pointed out, we don't know for sure unless we also factor in the weight of the bike. And since the bike weight is a larger proportion of the lighter rider's body weight, this adjustment should nudge the figures back in the favour of the heavier rider. Let's allow 8kg for bike plus clothing/shoes/helmet. In that case, we end up with 5.29W/kg for the lighter rider + bike and 5.05W/kg for the heavier rider + bike. The lighter rider still has a clear advantage and will climb faster.

On the flat, again assuming that we have sphere shaped riders, we have the following power to frontal area ratios:

90 kg rider : 495/0.2428 = 2,039W/m2
60 kg rider : 360/0.1853 = 1,942W/m2

In this case, the heavier rider has a clear advantage. The bike weight is irrelevant at a steady speed.

So there you have it. The lighter rider, with the slightly higher power to weight ratio, is faster on the climbs but slower on the flat.

Right, I'm away out for a spin.

[* Of course, for a given frontal area, the aerodynamic drag can vary a lot. But we're assuming here that riders are using very similar equipment and that their riding positions are similarly aerodynamically efficient]

Rofo

Blimey! Thanks, that all makes sense :-)

snailsong

I suspect the the optimal path on which to ascend the 100m will not be a straight line, but some sort of curve. In the initial phase the rider will have to accelerate so it may be even more efficient to begin on a slight downslope rapidly curving upwards and becoming a straight line once terminal velocity is achieved. Interestingly a family of curves called cycloids often crop up in this sort of problem.

I hope this clarifies and simplifies the matter.:)

Lumen

@Keep_Her_Lit your analysis is interesting but you can't diet yourself aero.

I would interpret your results as "short/aero people need significantly less power to sustain the same speed on the flat".

Inquitus

Howth Village side versus Sutton side is a good testbed for this. I think I am about 2 mins quicker up the village side from memory.

ROK ON

To add a practical dimension to this, would people prefer to climb a 20km climb averaging 5% (with a very low StdDev), or an 8km climb at 12.5% gradient.