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percentage true slope vs. road distance variation(16 posts)

percentage true slope vs. road distance variationDougSloan
Jul 2, 2003 2:09 PM
I was curious (as may be other anal types) about the error of calculating percentage slope using road distance traveled versus true rise over run (which is hard to measure).

Normally, when people calculate slope for hills, they just take the rise divided by the road distance. As we know, this is technically wrong, as the "run" aspect of the percentage calculation should be horizontal, not the road as it rises. The true horizontal will always be a shorter distance than the road distance on a climb, resulting in higher true percentage figures.

Turns out it's a pretty small error at slopes normally encountered, less than .5% for a 20% grade.

Here's a chart I made showing the difference. The true slope was calculated using the pythagorean theorem with the known sides of the road distance traveled as the hypotenuse and the rise (elevation change) as the other known side. If anyone sees any errors, please let me know.

Doug. Mellow out. Have a beer. Buy that Stumpjumper. (nm)mapei boy
Jul 2, 2003 2:16 PM
Jul 2, 2003 2:22 PM
Haven't you ever had something that bugged you for years, just wanting to know the answer but never taking the time to figure it out? This one had. Turns out, no big deal.

Bike should be in tomorrow. Friday morning should be on my way up to Shuteye Peak -- a 5,000 foot gain mtb ride from Bass Lake near here; mostly fire road, but with some really nasty rocky Jeep road sections. Nice lookout tower at the top. Haven't been on a mtb for 3 years, though.

Bugger Babychar
Jul 2, 2003 7:39 PM
Yep, as you have graphically demonstrated, insignificant in a 3 dimensional world.

Please recalculate using 4,5, and up to 11 dimensions...:)

I seem to have space time continuum warp at over 12%, my fat ass seems to go back in time as I move forward on the slope.

And its more fun to ride road bikes off-road. I've set up my old vintage Eddy for off-road rambling and the commuter sees dirt every day, it is just plain dog'on more fun on the alternative routes.

You have too much time on your hands and need to ride more.Humma Hah
Jul 2, 2003 2:19 PM
I've done that calculation and decided that the error is meaningless at slopes ordinary mortals, including you, can climb.
Thanks too lateDougSloan
Jul 2, 2003 2:23 PM
Thanks for nuttin.

Didn't take *that* long, even for a lawyer. ;-)

That's not true!Mel Erickson
Jul 2, 2003 6:03 PM
You said it's been buggin' you for years. I'd say that's a long time, especially for a lawyer.
Does anyone know that thing with a bubble for getting slope ?PeterRider
Jul 2, 2003 7:22 PM
Don't know how you call in english the tool which has a bubble in it, that you use to make things horizontal or vertical, like for instance when you tile a floor. So, I heard there is a similar thing that gives you the % slope. I guess you fix it to your bike and it basically measures the inclination of the bike. Does anybody know about this thing ?

Jul 2, 2003 7:36 PM
We call it a LevelAllUpHill
Jul 2, 2003 8:08 PM
What do you call it in French?

I have the velimpex gadget Doug points out. Kind of intriguing, but the only way to get a dependable reading is to get off the bike and hold it steady on the slope. And stopping, dismounting, and starting on a 20% grade isn't exactly easy...
"Niveau a bulle"PeterRider
Jul 2, 2003 8:39 PM
-> level with bubble.

the "dependable only if you hold it steady" is exactly what I feared. Thanks for the info. But the idea behind the gadget is nice.

Well it gives you something to do ...Humma Hah
Jul 3, 2003 6:47 AM
... when a hill gets the better of you and you just gotta stop. When someone sees you get off, you can swear that you just need to get a good reading on the grade of this climb, and that's the only way.

On more modest slopes, I would think that achieving a good reading would be a great way to train for a smooth stroke and steady technique.
still seems to meDougSloan
Jul 3, 2003 6:58 AM
Still seems to me that the bubble gizmo would work better if the liquid in it were just a bit thicker, so that the bubble moves freely, but more slowly. Wouldn't that be possible?

That would be one approach ...Humma Hah
Jul 3, 2003 7:52 AM
... essentially filtering the data to low bandwidth.

The other way to do it is high-speed sampling ... what we do with the accelerometers and altimeter on the flight control computer. Just read the thing about 2000 times a second and calculate the average.

That gives me a headache. Maybe if we put some oil in the tube, something like a 40-weight.
I dont think so ...AllUpHill
Jul 3, 2003 8:39 AM
More viscous fluid would stablize things for sure, but the bubble would not settle well in its correct position. The curvature of the lens isn't all that great, so the bubble would slowly approach the apex, but creep to a virtual halt before getting there in any reasonable amount of time.

Also, I didn't mean to imply it's worthless. Kind of fun to use for a while, at least until you get a good feel for the slopes of your local climbs. And getting a usably steady reading is not too hard if you're in the saddle, spinning smoothly on 10% or less. But, for the impressive grades toward 20% which you really care to measure, your both your head and the bubble are bobbing too much from the choppy effort. (I've only found one stretch at 20% where I live, and I had to dismount to read it for sure.)

Plus, ANY acceleration forward or backward alters the reading, so you have to make sure your speed is absolutely constant. For e.g., you're on a slight downhill, braking moderately toward a stop sign, and the bubble goes way back indicating a 20% downhill. Even the less drastic acceleration of coasting down a hill causes the bubble to move forward artificially.
I dont think so ...M_Currie
Jul 3, 2003 7:24 PM
I have one of these too, and the fluid is fairly viscous, but as you note, it has to be liquid enough to settle quickly too, and I think the compromise favors quickness over stability. I rode with mine on for a half season or so, then took it off, but it was kind of fun to get a reading on some local hills. On even climbs at steady speed you can get a pretty close guess by averaging as the bubble surges forward and back but the best way I found was to stop on the way down and get the reading there.