Working out how to measure 'steepness' of a hill...
Comments
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Ha. Cos I'm great, that's why.tarquin_foxglove wrote:
How do you work that out? :?:garrynolan wrote:Thanks for the replies. 1st = CiB. Joint 2nd = the rest. My head is no longer wrecked trying to understand this - Thanks again .
Our man Garry had the wrong of the stick in the first post so I clarified it for him, explaining how hills are described. What's that about shoving a fish in someone's direction to feed him for the day, or teach him to fish and feed him for life thus invoking an unhealthy lifetime fish-only diet purely to get him out of your hair for 10 minutes? 8)garrynolan originally wrote:If a hill is 45 degrees then logically it is a 50% hill. So, does this mean that a 20% hill is 72 degrees? This seems almost stupidly steep so am I doing this properly? Please help (in simple,easy to understand terms) as it's doing my head in.
Sorted anyway. Hills are either easy, manageable, strewth or Welsh. That's all we need.0 -
Lightning wrote:
Not sure if serious. The car could be a bike, a person or nothing at all. The purpose of this is just to represent what a slope is exactly.Pep wrote:Sure this must be wrong.
How can a car odometer measure the horizontal projection of the distance travelled?
A car odometer knows only how many turns the wheel did. So, the only distance a car can measure is the slope distance. Percentage is the SIN of the angle. Not the TAN.
:!:
It is.
No difference in this respect with car, or bike, or person.
How can you possibly measure the horizontal projection of the distance travelled? You can't.
What you measure is the distance traveled. And the altitude gained. That's why the percentage of a slope is the SIN of the angle. Not the TAN.0 -
Pep wrote:Lightning wrote:
Not sure if serious. The car could be a bike, a person or nothing at all. The purpose of this is just to represent what a slope is exactly.Pep wrote:Sure this must be wrong.
How can a car odometer measure the horizontal projection of the distance travelled?
A car odometer knows only how many turns the wheel did. So, the only distance a car can measure is the slope distance. Percentage is the SIN of the angle. Not the TAN.
:!:
It is.
No difference in this respect with car, or bike, or person.
How can you possibly measure the horizontal projection of the distance travelled? You can't.
What you measure is the distance traveled. And the altitude gained. That's why the percentage of a slope is the SIN of the angle. Not the TAN.
Sorry if I've got this hopelessly wrong because whenever the word 'calculus' was mentioned at school my eyes would glaze over and I transformed into the square of the hyperobtuse, but if you track the route on a map don't you get the horizontal projection of the distance travelled?0 -
deptfordmarmoset wrote:Pep wrote:Lightning wrote:
Not sure if serious. The car could be a bike, a person or nothing at all. The purpose of this is just to represent what a slope is exactly.Pep wrote:Sure this must be wrong.
How can a car odometer measure the horizontal projection of the distance travelled?
A car odometer knows only how many turns the wheel did. So, the only distance a car can measure is the slope distance. Percentage is the SIN of the angle. Not the TAN.
:!:
It is.
No difference in this respect with car, or bike, or person.
How can you possibly measure the horizontal projection of the distance travelled? You can't.
What you measure is the distance traveled. And the altitude gained. That's why the percentage of a slope is the SIN of the angle. Not the TAN.
Sorry if I've got this hopelessly wrong because whenever the word 'calculus' was mentioned at school my eyes would glaze over and I transformed into the square of the hyperobtuse, but if you track the route on a map don't you get the horizontal projection of the distance travelled?
Correct! :P
If you track the distance travelled ON A MAP. But is this really the way you do it? You ride 100km Sunday morning with your mates and then to know the distance travelled you TRACK IT ON A MAP?
I know the distance travelled by reading the odometer. If flat, the two are identical. If slope, the distance measured by the odometer is (slightly) LESS then the one measured ON THE MAP.
gradient = altitude gain / distance travelled = SIN(angle)
altitude gain / map distance = TAN(angle)
distance travelled = the one measured by the odometer
MAP distance = odometer distance ONLY IF FLAT.
Map distance < odometer distance IF NOT FLAT.0 -
If you have height and distance travelled, which is measured by odometer then the angle would be calculated using SIN.
If however, you have horizontal distance (from a map) then the angle would be calculated using TAN
In practical terms it doesn't actually matter if you use SIN or TAN because you wont find any roads over 33%.
SIN(x) is approximately equal to TAN(x) for small angles
33 % = 18.26 degrees
SIN(18.26) = 0.331
TAN(18.26) = 0.333
which is 6 % error for the most extreme road you'll ever encounter. For more typical gradients of 5 - 15% there's hardly any noticeable difference.
Thus the approximation Gradient = height / (distance measured by odometer)
is more than good enough0 -
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sfichele wrote:If you have height and distance travelled, which is measured by odometer then the angle would be calculated using SIN.
If however, you have horizontal distance (from a map) then the angle would be calculated using TAN
In practical terms it doesn't actually matter if you use SIN or TAN because you wont find any roads over 33%.
SIN(x) is approximately equal to TAN(x) for small angles
33 % = 18.26 degrees
SIN(18.26) = 0.331
TAN(18.26) = 0.333
which is 6 % error for the most extreme road you'll ever encounter. For more typical gradients of 5 - 15% there's hardly any noticeable difference.
Thus the approximation Gradient = height / (distance measured by odometer)
is more than good enough
True.
Because angles are small TAN and SIN are almost the same.
But still, why would you bother with MAP distance when odometer distance is much more easily available?0 -
Yes - but in practical terms it doesn't matter!
Lets say you do a 1 km climb at 10%. Distance measured by odometer is (obviously) 1 km.
The horizontal distance is 995m which is a 0.5 % error0 -
Having done a 20 mile-ish hill walk up some severe slopes I decided I was being robbed and that the actual distance must be far more than the plan distance. I did a lot of calculations and found that the difference was negligible, I was devastated!
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sfichele - your avatar is showing how much I understand this now. Thought I had it but now my head hurts! Didn't do Binary at school - must've missed TAN/SINE stuff as well...Visit Ireland - all of it! Cycle in Dublin and know fear!!
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Its really simple (honest). tarquin_foxglove's post and CMat59's post had everything you needed to know in a nice simple diagram.
Forget about SIN and TAN its complicating things. Also, for practical examples there is very little difference between horizontal distance and odometer distance, so don't let that baffle you.
Just take the height that you gained and divide it by the horizontal distance travelled
gradient = height_gained / horizontal_distance_travelled
Example 1:
If you gain a height of 100m, and travelled 1000m then gradient = 100/1000 = 0.1
0.1 is the same as 10 %
The angle is atan(0.1) = 5.7 degrees
Example 2:
If you gain 200m, and travelled 1000m then gradient = 200/1000 = 0.2
0.2 is the same as 20 %
atan(0.2) = 11.3 degrees
Example 3:
If you gain 10 m, and travelled 400m then gradient = 10/400 = 0.025
0.025 = 2.5 %
atan(0.025) = 1.4 degrees
Example 4:
A more extreme example.
If you gain 1000 m in height and your horizontal distance is also 1000 m
then gradient = 1000/1000 = 1.0 = 100 %
atan(1.0) = 45 degrees
Hope that clears it up0 -
Which is exactly wot I wrote. All this business of using SIN & TAN is just adding to the confusion, and is unnecessary in the context of the original question.Just take the height that you gained and divide it by the horizontal distance travelled
gradient = height_gained / horizontal_distance_travelled
Example 1:
0.1 is the same as 10 % (= 1 in 10)
Example 2:
0.2 is the same as 20 % (= 1 in 5)
Example 3:
0.025 = 2.5 % (= 1 in 40)
Hope that clears it up
Anyway. Carry on. It's good this is.0 -
Yeh - sure the SIN and TAN stuff adds confusion. I was just trying to show that for practical examples there is very little difference between odometer distance and horizontal distance. Also there was some slightly incorrect info above.
However, the opening question did talk about angles so SIN and TAN are actually relevant.
Really there is nothing more to it than:
SIN ( ANGLE ) = rise / odometer_distance
TAN (ANGLE) = rise / horizontal_distance = gradient0 -
You don't seem to understand why I posted that image. The purpose of the image was to show what a slope is, and what it means. You're assuming I'm telling you to go on a ride and calculate slope like that when I'm not. I just figured the image was clear enough to understand the concept of slope (apparently it wasn't).Pep wrote:It is.
No difference in this respect with car, or bike, or person.
How can you possibly measure the horizontal projection of the distance travelled? You can't.
What you measure is the distance traveled. And the altitude gained. That's why the percentage of a slope is the SIN of the angle. Not the TAN.0 -
garrynolan wrote:sfichele - your avatar is showing how much I understand this now. Thought I had it but now my head hurts! Didn't do Binary at school - must've missed TAN/SINE stuff as well...
just remember garynolan there are only 10 types of people in world.....those who get binary and those who don't.The dissenter is every human being at those moments of his life when he resigns
momentarily from the herd and thinks for himself.0
