gradient of a hill

Quoted post said:

Originally posted by Jakebrake
Could someone tell me what the formula is to determine what the percentage gradient of a hill is? Thanks 🙂

A bit of basic maths. Imagine the hill is the long part (hypotenuse) of a right angle triangle. Measure the vertical distance of the hill (assume a straight line) divide this by the horizontal distance . Multiply that by 100 and there is your percentage. Let's assume the height of the hill from start to finish is 100m and horizontal distance is 1000m. 100m/1000m = 0.1 X 100 =10% (a bloody hard grind).

However since you can't measure the horizontal distance directly, you can apply the Pythagorus theorum. You should have been taught this in high school. You can measure the hypotenuse (h)on your bike computer (ie the distance travelled). You may be able to measure the height of the hill (b) using an altimeter (some bike computers have them. Now you know the hypotenuse and one of the other two sides. Pythagorus theorum is that the square of the hypotenuse equals the sum of the squares of the other two sides. h2 = a2 + b2 where h is hypotenuse length, a is horizontal distance and b is height. Knowing these you can apply the formula.

Say our hill is a 5 km ride to the top (ie the distance of the hypotenuse, h) and the height of the ride (b) from start to finish is 200m. The formula we need is 5,000 x 5,000 = (200 x 200) + (a x a) where a equals the horizontal distance of the triangle. That is 25 million = 40 thousand + a squared. Then a squared = 25 million - 40 thousand (24,960,000). a = square root of 24 960 000 = 4,996. To get percentage grade of hill = b/a x 100. So 200/4996 x100 = 4% (should be able to do that one in the middle gears).

All this would be simplr if I could draw a diagram.

You can use trigonometry, but I'm too tired to remember how to do it, and can't be bothered looking up a text book. It involves measuring the angle of the hill using a clinometer. I'm sure some other bright spark will enlighten us.

Thank you very much Spider for your reply. You are indeed the "bright spark" I was searching out for. You have brought forth the information I was seeking.

There is a hill that I climb that is 1.6 km in length, and rises 351 meters. I believe if I followed your formula correctly, that would work out to about a 22% grade.

Quoted post said:

Originally posted by Jakebrake
Thank you very much Spider for your reply. You are indeed the "bright spark" I was searching out for. You have brought forth the information I was seeking.

There is a hill that I climb that is 1.6 km in length, and rises 351 meters. I believe if I followed your formula correctly, that would work out to about a 22% grade.

That's a pretty steep hill! There was a thread somewhere on this site where we had a bit of a debate over the best way to measure the gradient, but I can't remember where it was... oh well, spider's explanation is exemplary anyway!

Yes Jakebrake, you have calculated correctly. 22% is very steep. Your nose would just about be scraping on the front wheel. I don't think I'd be able to get up a hill that steep even in a 39-25 combination on my road bike. What gear do you use?

Hey I might be bright, but it doesn't seem to translate into being a good race tactician!

22% would knock my face off. Imagne that with a headwind, you'd rip your back out i think. major hard

I use a 39-25. It's a road that leads up into a few tech company businesses, then further up into a subdivision. It's off the main route that I ride, and every other week or so I'll give it a go just to see that I can still do it. It's a killer, it will stick your heart right up into your throat. Momentum is non-existant. I'm never so glad as to when I finally crest over.

Can you ask the city to post a yellow (% gradient) sign warning cyclists of a major nose bleed area?!?!? We have those lovely lil signs in our mountains here in Colorado - which is usually way too late as you sail through the switch-backs in mid-air!!

I can understand why there are only tech company businesses at the top of that hill. I couldn't see a hevily laden truck getting up it.

It must be fun to come down. What speed do you do going up and how frightening is it coming down?

On the way up on the steeper sections, I'm motoring along at an almost falling over sideway pace of 5.5-6.0 mph, on the way down I'm brakin' it and keeping it around 35 mph. There are a few slight curves, side streets and business entrances that I kind of worry about.

On the west side of our city, we have the Texas Hill Country. The hillsides are jam packed with very high dollar houses. Everyone wants to live on a hill. The Problem is to build subdivions in these areas, you basically have to build a road that goes straight up to get there. I drive a truck for a living and back in the mid 90's I use to haul brick. Talk about "pucker factor", I'd be grossed out at 80,000 lbs, I'd grab my "granny gear" and crawl up these things. It was very unsettling, wondering if you would make it. My tractor had a 4 1/4 Cat, and it always made it up just fine, but you know how the mind works, you start thinking, "What if I peg out before I make the crest, what do I do?" 🙂