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Old 07-03-08, 10:41 AM   #1
kkp
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Why is riding uphill at say 7.deg incline, soooo much harder than 5.deg incline.

Why does a small change in incline angle make so much difference?

Here is the answer... Please note this will get a little bit mathematical. However I have kept it simple as possible.

In summary, this is because a greater component of your weight is working against you by dragging you downwards. This component of your weight increases out of proportion with the angle of climb.

For those who don’t need math or physics based explanation can stop reading now. Of course I would welcome corrections to this – I worked this out using the physics learnt at school.


Basically the force of gravity that works in the downward direction of the slope is:

Force = Mass * Gravity * Sine (Angle)

So if you are a 70kg person, climbing at 5deg:

Force = 70 * 9.8 * Sine (5deg) = 59.79 Newton (a unit of force)

The same person climbing at 7deg

Force = 70 * 9.8 * Sine (7deg) = 83.60 Newton

So this small change in angle has added almost 24Newtons of downward force that you have to work against.

It is interesting to look at it this way – How much weight should
I loose in order to make the 7deg incline feel like 5deg .. by shedding weight I effectively reduce the downward force working against me.

Basically I now want the following equation to hold true.

Force = MyNewWeight * 9.8 * Sine (7deg) = 59.79

MyNewWeight must reduce so that the force I experience is the same as I would experience at normal weight.

The answer: ... 50kg!! ... I would have to loose 20Kg! just to make 7deg feel like 5deg.

Of course results will vary with the angle.

For example to make 12deg feel like 10deg, I would need to loose 12kg.

Dragging 58kg up a 12deg slope is same work as dragging 70kg up 10deg slope.

Unless already overweight (and since you are a cyclist you arent right ) this is one
tough call.
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Old 07-03-08, 11:06 AM   #2
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"Unless already overweight (and since you are a cyclist you arent right )"


...I'm guessing you've never been to an organized Metric Century!



it is interesting, though, how much harder a couple of degrees makes a climb, though.

Where I live, there are alot of sections that are in the 15% - 20% range. Those sections may only be for a quarter mile or so, but boy can it beat you up over the course of an afternoon.

I did similar sets of equations comparing the amount of power needed to go just one mph faster at 10%, 15% and 20% grades for my current body weight, and if I lost 10 pounds

Its amazing how when the grade really goes up how much power it takes to go a little faster, or carry a little more weight, or as in your case, climb a slightly steeper angle.

I guess it all goes back to the acceleration of gravity being an exponential force so the increases in power are non-linear

nice break down
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Old 07-03-08, 11:29 AM   #3
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Uhhhh, you're calculations look good, but a 5 deg incline is a 10% grade. A 7 deg incline is a 14% grade. Have another look.

For reference, a 45 degree incline is a 100%grade.
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Old 07-03-08, 01:00 PM   #4
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Quote:
Originally Posted by JoelS View Post
Uhhhh, you're calculations look good, but a 5 deg incline is a 10% grade. A 7 deg incline is a 14% grade. Have another look.

For reference, a 45 degree incline is a 100%grade.
A 5 deg incline= 8.7% grade and 7deg= 12.3, but that doesn't change what the OP did. - TF
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Old 07-03-08, 01:03 PM   #5
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Old 07-03-08, 01:09 PM   #6
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A 5 deg incline= 8.7% grade and 7deg= 12.3, but that doesn't change what the OP did. - TF
I see where I was wrong. Thanks for the correction.
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Old 07-03-08, 10:19 PM   #7
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Not only are roads usually measured with gradient (rise/run), the math is a lot easier to deal with.

As an example, comparing a 5% hill to a 7% one, the 7% hill is 7/5 = 1.2 = 20% harder than 5% one. You can climb it at the same speed with 20% more power, or 20% slower at the same power.

That's a rough approximation - it assumes that you have low enough gearing to ride at the same cadence. If you could climb that 14% hill at the same cadence as a 7% one, it would be just as hard (but at half the speed). But you generally don't have that gearing, and having to ride at a reduced cadence is a lot harder.

That's also ignoring that different muscle recruitment you get on steep hills and the difficulty of keeping a smooth pedal stroke at higher pedal forces.
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Old 07-04-08, 09:49 PM   #8
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A lot of math to say steeper hills are harder to ride.
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Old 07-07-08, 06:16 PM   #9
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There is no such thing as gravity... the world sucks.
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