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Degrees? Percentages?

Old 03-26-21, 07:43 AM
  #26  
ofajen
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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
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Old 03-26-21, 07:45 AM
  #27  
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Originally Posted by wphamilton
I think it just needs a diagram to be made clear:

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>
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Old 03-26-21, 08:03 AM
  #28  
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Originally Posted by Iride01
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>
You like to stir up "math" controversy don't you? Me too.

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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Old 03-26-21, 08:12 AM
  #29  
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Originally Posted by wphamilton
I think it just needs a diagram to be made clear:

*ahem* Post #9 above.
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Old 03-26-21, 08:13 AM
  #30  
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Originally Posted by wphamilton
You like to stir up "math" controversy don't you? Me too.

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.
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>
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Old 03-26-21, 08:27 AM
  #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.

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Old 03-26-21, 10:18 AM
  #32  
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Originally Posted by DaveSSS
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.
It may not be possible to measure real horizontal distance, but it can be determined through trigonometry. In any case, the common referents for slope/grade have no purely linear relationship.

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Old 03-26-21, 11:55 AM
  #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.)
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Old 03-26-21, 11:58 AM
  #34  
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And to think I started it all!

Originally Posted by Iride01
Grade will certainly be the next big controversy.
I'm humbled at the recognition of my small part in the advancement of human understanding of hypotenteutical euclidian distance.
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Old 03-26-21, 12:05 PM
  #35  
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Originally Posted by Troul
kick it in the 52/11 with a 10 mph or higher headwind to simulate the climb.
As a comparison example, two regular parts of my rides these days are climbing several 5% hills at about 12 mph and riding 15 mph on level ground into the usual 12 mph headwind this time of year. They have about the same power requirement of 300 watts.

Otto
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Old 03-26-21, 12:10 PM
  #36  
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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.
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Old 03-26-21, 12:11 PM
  #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/
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Old 03-26-21, 12:16 PM
  #38  
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Originally Posted by UCantTouchThis
Carry one of these with you. Only $9, slimline structure and light weight.

If nobody said it yet, this makes me think if there is a phone app that would display both measures (would need to have the phone attached on bike and calibrated), or maybe some cyclo computers might provide such readout?
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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Old 03-26-21, 12:37 PM
  #39  
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Originally Posted by Elbeinlaw
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/
Partly you are still wanting to collapse the different quantities of angle and slope.

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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Old 03-26-21, 12:55 PM
  #40  
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Originally Posted by ofajen
Partly you are [asking the] sensible question of why a right angle is 90 degrees
But Otto, we all know why that is! That's what my protractor says it is. Right?
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Old 03-26-21, 01:36 PM
  #41  
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Originally Posted by Elbeinlaw
So I wonder why our intellectually giant forebears choose this formulation/
Probably because rise:run was easy to work out quickly on the job site.
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Old 03-26-21, 02:06 PM
  #42  
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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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Old 03-26-21, 03:18 PM
  #43  
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Originally Posted by Iride01
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>
It can't be much longer until someone (who just bought a GPS earlier in the month) drops by to tell us there's a mismatch between his new GPS and the surveyed maximum grade on a hill nearby, and obviously the GPS is right. Electronics! Satellites!
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Old 03-26-21, 04:59 PM
  #44  
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Originally Posted by downtube42
I used to have a carpenter buddy who'd say he didn't understand math, but flawlessly calculated construction dimensions. He's shrug and say it was just numbers.
lol...I knew a few like that
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Old 03-26-21, 07:03 PM
  #45  
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Originally Posted by Elbeinlaw
What I want is to be able to translate--approximately, and in very broad strokes--percentages to degrees, or degrees to percentages
Approximately? In broad strokes?

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.
That's a broad stroke approximation. If you don't want to worry too much, forget the tiny amount. Here's an exact table from msu2001la

Originally Posted by msu2001la
1 degree = 1.8%
2 degrees = 3.5%
3 degrees = 5.2%
4 degrees = 7.0%
5 degrees = 8.8%
6 degrees = 10.5%
7 degrees = 12.3%
8 degrees = 14.1%
9 degrees = 15.8%
10 degrees = 17.6%
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Old 03-27-21, 07:28 AM
  #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?
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Old 03-27-21, 12:58 PM
  #47  
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What I wanna know is, why are the uphills steeper and longer than the downhills?
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Old 03-27-21, 03:55 PM
  #48  
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Work in radians instead of degrees and the math becomes trivial.
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Old 03-27-21, 03:58 PM
  #49  
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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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Old 03-27-21, 05:37 PM
  #50  
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Originally Posted by Trsnrtr
As a retired highway engineer, I can honestly say that I never measured or referred to a grade using degrees.
I think it’s become more of a common measurement for people to see with vehicles that now have onboard sensors that measure slope in degrees. I’ve only seen % grade shown on road signs.

Otto
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