Degrees? Percentages?
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I just figure 1.75% of grade for each 1 degree.
The exact number is a tiny bit less (1.7455%), but it’s a good approximation for any hill I would ever tackle. For truly steep angles, the grade starts to increase progressively more per degree, but those angles aren’t usually relevant for bikes.
Otto
The exact number is a tiny bit less (1.7455%), but it’s a good approximation for any hill I would ever tackle. For truly steep angles, the grade starts to increase progressively more per degree, but those angles aren’t usually relevant for bikes.
Otto
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Shssssh, Hush!
Your diagram is going to make too much too clear. Now we are going to have people wondering about the accuracy of the grade from their GPS because they'll wonder if it's going by the distance traveled on the hill (Hypotenuse) or horizontal distance (Adjacent side) ! <grin>
Your diagram is going to make too much too clear. Now we are going to have people wondering about the accuracy of the grade from their GPS because they'll wonder if it's going by the distance traveled on the hill (Hypotenuse) or horizontal distance (Adjacent side) ! <grin>
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Shssssh, Hush!
Your diagram is going to make too much too clear. Now we are going to have people wondering about the accuracy of the grade from their GPS because they'll wonder if it's going by the distance traveled on the hill (Hypotenuse) or horizontal distance (Adjacent side) ! <grin>
Your diagram is going to make too much too clear. Now we are going to have people wondering about the accuracy of the grade from their GPS because they'll wonder if it's going by the distance traveled on the hill (Hypotenuse) or horizontal distance (Adjacent side) ! <grin>
FWIW, for small angles, sine and tangent are close enough not to matter. So if it's easier for anyone to use arcsine than arctan, I say have at it.
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Grade will certainly be the next big controversy. <big GRIN>
#31
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All I need to know is that 4% and under isn't difficult, but 10% requires my lowest gear if it's a very long stretch. I've measured some of my 10% grades with a digital level.
Percent grade is really vertical rise divided by horizontal run, but it's not possible to measure horizontal on a road, so it's vertical rise divided by the length of the road. On small angles, it's close enough. Road lengths in the mountains are not measured horizontally.
Percent grade is really vertical rise divided by horizontal run, but it's not possible to measure horizontal on a road, so it's vertical rise divided by the length of the road. On small angles, it's close enough. Road lengths in the mountains are not measured horizontally.
Last edited by DaveSSS; 03-27-21 at 08:27 AM.
#32
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#33
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Bulette: Thank you, thank you, thank you. I'd plum* run out of jargon to pepper my patter. But now, "Euclidian distance" is going to be my new buzzword. May add "hypoteneutical," "arctan" and "arcsin" too, in case anyone's in danger of catching on that I'm speaking nonsense. I find that once the geometry comes out, the attention disappears.
(*pun ntended.)
(*pun ntended.)
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Otto
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Go to the App store on your smartphone and download "Clinometer" (free). You tilt your phone, it can show you what the tilt is in degrees / percent.
#37
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A thought about intellectual history
Thank you all for your input. You've answered my question, given me more jargon to foist on unsuspecting persons, and made some interesting points about ... stuff. In pondering this--can't ride today, so have to think--I'm fascinated by how 45% became 100%. On the one hand, it's obvious: if you're looking at Euclidian geometry, then a rise/run where rise=run just naturally seems like it would be x/x, or 1, or 100%.
But if you're doing anything practical in the real (nonEuclidian) world, it doesn't make any sense. If you're roofing, a 45 degree/100% slope isn't the highest a roof can effectively be: that's going to be something like 60 degrees (thinking of those snow roofs in Switzerland). And how would you describe those roofs, even outside of the problem of Hochdeutsch? They'd have to be something like 140%, which makes no sense, because they're steep but not outside the bounds of reality. In an alternate universe, it would seem to me like if you started with practical reality, where percentages were representations of the proportion of a "whole," whatever that is, you'd say that a 100% slope would be 90 degrees--it's the highest a slope can go before it's no longer a slope at all. (And that would make sense in roofing, because a 60% slope would then be something like (just guessing here) 75 degrees.) And a 0% slope would be 0 degrees. That seems to me to be imminently more intuitively sensible.
But for some reason, our forebears decided that practicalities weren't the focus of this datum, it was the arithmatic fraction substituting for the rise/run formulation.
So I wonder why our intellectually giant forebears choose this formulation/
But if you're doing anything practical in the real (nonEuclidian) world, it doesn't make any sense. If you're roofing, a 45 degree/100% slope isn't the highest a roof can effectively be: that's going to be something like 60 degrees (thinking of those snow roofs in Switzerland). And how would you describe those roofs, even outside of the problem of Hochdeutsch? They'd have to be something like 140%, which makes no sense, because they're steep but not outside the bounds of reality. In an alternate universe, it would seem to me like if you started with practical reality, where percentages were representations of the proportion of a "whole," whatever that is, you'd say that a 100% slope would be 90 degrees--it's the highest a slope can go before it's no longer a slope at all. (And that would make sense in roofing, because a 60% slope would then be something like (just guessing here) 75 degrees.) And a 0% slope would be 0 degrees. That seems to me to be imminently more intuitively sensible.
But for some reason, our forebears decided that practicalities weren't the focus of this datum, it was the arithmatic fraction substituting for the rise/run formulation.
So I wonder why our intellectually giant forebears choose this formulation/
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But that doesn't address the OPs query of getting some idea of the meaning of numbers on his map. But a phone app or some easy conversion chart should exist?
Last edited by vane171; 03-26-21 at 12:20 PM.
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In an alternate universe, it would seem to me like if you started with practical reality, where percentages were representations of the proportion of a "whole," whatever that is, you'd say that a 100% slope would be 90 degrees--it's the highest a slope can go before it's no longer a slope at all. (And that would make sense in roofing, because a 60% slope would then be something like (just guessing here) 75 degrees.) And a 0% slope would be 0 degrees. That seems to me to be imminently more intuitively sensible.
But for some reason, our forebears decided that practicalities weren't the focus of this datum, it was the arithmatic fraction substituting for the rise/run formulation.
So I wonder why our intellectually giant forebears choose this formulation/
But for some reason, our forebears decided that practicalities weren't the focus of this datum, it was the arithmatic fraction substituting for the rise/run formulation.
So I wonder why our intellectually giant forebears choose this formulation/
Underlying that, however, is the sensible question of why a right angle is 90 degrees. There is a unit called the gradian and a right angle is 100 gradians. You would probably prefer that.
But the Babylonians really liked base 60 math and they left their imprint on how we divide up circles into 360 degrees, rather than 400 gradians (or 2 x pi radians, as is done in SI units and most areas of math).
Besides, 360 is pretty handy because it is highly composite, meaning it can be divided a lot of ways. Same is true for 90 degrees, which can be divided by 1,2,3,5,6,9,10,15,18,30 and 45 (11 distinct ways). 100 can be divided by 1,2,4,5,10,20,25 and 50 (8 distinct ways).
i might have made the case for 120 degrees, which is divisible by 1,2,3,4,5,6,8,10,12,15,20,24,30,40 and 60 (15 ways!). But that was a while ago.
Otto
Last edited by ofajen; 03-26-21 at 12:42 PM.
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Well if you did run over rise you'd have large numbers representing the shallower slopes. Whether that's part of the why, I don't have any idea.
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Yeah, it used to be people worrying over their Calorie count saying 900 for a ride but another persons device said 850 Calories burned for the same ride. And now we see similar arguments about power meter readings.
Grade will certainly be the next big controversy. <big GRIN>
Grade will certainly be the next big controversy. <big GRIN>
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lol...I knew a few like that
#45
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Okay, here's an approximate rule that gets you within a percent or two for converting percent grade to degrees.
- Take percent grade, divide it in half. Add a tiny amount. That's the grade in degrees.
- To get percent grade from degrees? Double the degrees, and subtract a tiny amount.
#46
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Yeah, but how long is this hill? Am I gonna get my interval finished before it peaks out or am I wasting my time?
#47
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What I wanna know is, why are the uphills steeper and longer than the downhills?
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Work in radians instead of degrees and the math becomes trivial.
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As a retired highway engineer, I can honestly say that I never measured or referred to a grade using degrees.
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