Calculating % Grade of a Hill

[Mr. Bloom]

I'm playing around on routeslip.com trying to plan out some routes.

I'm interested in focusing on hills, but I'm curious how slope translates in % grade. For instance, a road sign will say "10% grade"

If I'm looking at a route that rises 300 feet in 2 miles, what does that mean in terms of % grade?

Anyone know how to convert this?

[uforgot]

I'm playing around on routeslip.com trying to plan out some routes.

I'm interested in focusing on hills, but I'm curious how slope translates in % grade. For instance, a road sign will say "10% grade"

If I'm looking at a route that rises 300 feet in 2 miles, what does that mean in terms of % grade?

Anyone know how to convert this?

It would be the slope of the hill written as a %. Rise over run. The run is 2 miles, but you need to change it to feet. 10,560 ft for the run and 300 ft for the rise. 300/10,560 = .028409 or 2.84% grade.

Gosh, can't wait to tell my Algebra students that once again, I used it in my daily life!

[susan.wells]

Claudia is correct. Here is a link that gives a little detail --> grade.

[kelownagirl]

And here's a link that does the calculations for you.


http://www.csgnetwork.com/inclinedeclinegradecalc.html

[Mr. Bloom]

Thanks Ladies!

[uforgot]

Well, I'm standing in front of my geometry class, telling them how I used slope in an actual application, and I mention also that I have a new GPS and we can figure out the grade of a hill I rode Saturday. The hill is one block away, and they're going "what the heck, let US do it!"

With tape measures and my GPS we took measurements and the change in elevation. We did several hills. (Hey it's the first time we've had sunshine in months!). We came in, drew it out and someone notes "hey, our measurements are actually the hypotenuse, for run we have to use the pythagorean theorem!". It certainly was a proud moment for me. They proceeded to calculate the grade of 3 hills, and one student noted that you can't till a hill higher than 10%. (Farming community). They had a blast today, and I'd be willing to bet that they think about this sometime when they are driving up or down a hill.

Thanks for the idea! Now, how often do I have to use this GPS in order to make it tax deductible?

[RoadRaven]

Well done on making a subject interesting and memorable.

Always take the opportunity for something different...

My most memorable teacher was a maths teacher, and I didn't like maths much although I could do it ok.

He used to do interesting things, like take us to the park when the monarches were migrating. And we'd sit there with our calculators and formula books working out cosines and tangents!

You have given your students a day of learning they will most likely remember, a day that will influence some of them over their lifetimes.

They will not only be calculating and estimating gradients, they will also have a new respect and understanding of cyclists and runners who charge up these inclines - and a deeper understanding of you.

[Mr. Bloom]

Thanks for the idea! Now, how often do I have to use this GPS in order to make it tax deductible?

That's cool! As for 'tax deductible', forget that...that's just a 'discount'. Get the principal to reimburse the entire thing instead!

I'm convinced that kids respond well to practical learning when enhanced with technology. It's cool that you cared enough to speak to them in 'their language'.

[Chile Pepper]

That's what I thought the calculation was, but then the hill gradients seem really low. A 100% slope would be a 45 degree angle in terms of the hypotenuse of a right triangle. I see people talking about, say, a 10% slope as being difficult, but that would only be 4.5 degrees. I see stuff all the time that looks a lot steeper than that--and I'm not tallking about switchbacks, here. I'm not a spectacular climber, so I'm confused about eyeballing the angle of a slope. Are my eyeball estimates totally off? What would the slope of a hypothetical very-steep-but-climbable section be?

[mimitabby]

yes, 45 degrees is a 100% grade because you are travellling as far forward as you are up.

m not a spectacular climber, so I'm confused about eyeballing the angle of a slope. Are my eyeball estimates totally off? What would the slope of a hypothetical very-steep-but-climbable section be?

I'm really not sure what you consider climbable, but an 8% grade LOOKS formidable
and a 16% grade is tough to walk up and down, and both are climbable by some people.

I don't eyeball them, I have an inclinometer on my bike and my husband has a GPS that's how we figure it out

[Chile Pepper]

Thanks! That little device looks great. I think I'll try it out.

[Zen]

This thread makes my head hurt.

[mimitabby]

ah, come on. Walk 10 feet... now if when you get to the end of the 10 feet you are 2 feet higher than you were in the beginning, that's a 20% grade.

[lacyliz]

I tried calculations- yes, they work. But Specialized, Blackburn and others sell cyclocomputers that give you the %grade of a hill (altimeter feature), feet of elevation, etc. They're fantastic and this way you could compare your hills to hills on other rides, practice the % grade you want and everything. They run about $100, but well worth it (most have cadence, time, mph and everything you could possibly want)

[uforgot]

ah, come on. Walk 10 feet... now if when you get to the end of the 10 feet you are 2 feet higher than you were in the beginning, that's a 20% grade.

Careful! It's not quite as easy as that. If you walk up 10 feet and have risen 2 feet, your horizontal displacement is not 10, it's 9.8, which makes it 20.4%. Not an issue for a small rise, but it certainly is if the rise gets larger! If you walk up a 10 feet slope and rise 5, (30 degrees) it's not 50%, but 57%!

Remember when your Geometry teacher taught you the Pythagorean Theorem and you wondered..."when am I EVER going to use this?" Well, here ya go.