How roads are graded

vl1016 said:

What exaclty does a % grade mean? How do you knwo what grades of roads in yor area are? None of the big hills in my area have signs that tell you the grade, and they do not seem to be in maps either. How does a grade compare to an angle, ie, what would a 35 degree angle be grade wise? Thanks for the help.

It is rise over run expressed as a percentage. If the hill rises in alltitude 8 ft and covers a distance of 100 ft as the crow flies then that is 8/100 or 8%. Its important to note that the 100 ft is not the distance travelled along the road, but the level horizontal distance between two points. If you think of it in terms of a right anlge triangle then the hypotenous is the distance travelled along the road and the rise and run are the two legs connecting at the right angle.

To measure this yourself you would need to get the rise or difference in alltitude of two points and then measure the distance travelled along the road which is the hypotenous. Then use the pythagorean theorem to get the run. Then you can calculate the average grade between the two points. The angle of the hill is the arc-tangent of rise/run.

davidbod said:

It is rise over run expressed as a percentage. If the hill rises in alltitude 8 ft and covers a distance of 100 ft as the crow flies then that is 8/100 or 8%. Its important to note that the 100 ft is not the distance travelled along the road, but the level horizontal distance between two points. If you think of it in terms of a right anlge triangle then the hypotenous is the distance travelled along the road and the rise and run are the two legs connecting at the right angle.

To measure this yourself you would need to get the rise or difference in alltitude of two points and then measure the distance travelled along the road which is the hypotenous. Then use the pythagorean theorem to get the run. Then you can calculate the average grade between the two points. The angle of the hill is the arc-tangent of rise/run.

damn the roads I train on sometime most be about 15 16 %, and there is about 6 or 7 of them in a row

davidbod said:

Its important to note that the 100 ft is not the distance travelled along the road, but the level horizontal distance between two points.

Although this is correct technically (geometrically), keep in mind that in practice the difference between the distance travelled along the slope (the hypotenuse) and the horizontal distance between the two endpoints is very small for the tiny angles that represent the grades that mortal men can climb.

For example, even if you take a grade of 20%, which is *enormous*, applying the Pythagorean Theorem, the length of the hypotenuse would be:

hyp^2 = 100^2 + 20^2
hyp = 101.98

So, had the distance along the slope been used for the grade calculation instead of the pure horizontal distance, the grade would have been computed as:

(20 / 101.98) * 100 = 19.61

representing an error (underestimation) of 2%.

That is already a negligeble error margin (are you really measuring distance and/or elevation more accurately than 2%?) and for the more likely grade ranges that we all ride (say, 3% - 15%), the error percentage becomes even smaller.

This concludes today's math lesson. Now back to riding. 🙂

Berend

vl1016 said:

What exaclty does a % grade mean? How do you knwo what grades of roads in yor area are? None of the big hills in my area have signs that tell you the grade, and they do not seem to be in maps either. How does a grade compare to an angle, ie, what would a 35 degree angle be grade wise? Thanks for the help.

Another way to measure this it's to get a GPS, a Polar 710 (720, 725) or a equivalent bike computer with altimeter and let them do the calculations 😄

You might also want to try looking at topographical maps:

topozone.com

terraserver.microsoft.com

You should be able to make some sort of estimation on grade.

chemcycle said:

You might also want to try looking at topographical maps:

topozone.com

terraserver.microsoft.com

You should be able to make some sort of estimation on grade.

Thanks for all the replies! I'll check out the topo sites. I think I ride some serous grades.

thanks for the links
ok heres a basic ride where I live
useing "fasl" as Feet above sea level
it's short ok 🙂
1.my house it at 900fasl then up the driveway 600ft long to 910fasl
2.down small hill on gravel road drop to 880fasl and back up to 900fasl in 1/16 mile
3.then out to end of road 3/16 mile and then a drop to 850fasl in last 100foot of road
4.then down next road droping to 820fasl and then up to 880fasl last 200foot till turn again
5.then up small rise to 890fasl and slowly drop to 800ft over next 1/4 mile
6.then back up to 920fasl in next 1/4 and slight drop to 910fasl at next turn
7.then over next mile drop to 850ft at store
then back home again 🙂
2.6 mile one way
now tell me what grades I'm riding 😕 😄

If you know the distance you traveled and the vertical feet you climbed (if you have an altimeter), you can use a simple formula to calculate grade in percents and also incline in degrees.

I made a simple Excel spreadsheet to demonstrate.

click here and save it to your PC

.

sorebutt said:

If you know the distance you traveled and the vertical feet you climbed (if you have an altimeter), you can use a simple formula to calculate grade in percents and also incline in degrees.

I made a simple Excel spreadsheet to demonstrate.

click here and save it to your PC

.

dont have Excel 🙂

it means what percentage of the day the workmen spend on rolling it with the steam roller before their break, then after it depending on how many men there are for that particular section of the road and whether or not its a Monday or a Friday whereby there will be at least a few sickies to factor in. In addition if the foreman visits you will automatically lose 4 hour (or 8.5%) just for his/her presence and trying to do a "proper" job.

cuervo said:

Another way to measure this it's to get a GPS, a Polar 710 (720, 725) or a equivalent bike computer with altimeter and let them do the calculations 😄

This is precisely what I do (minus the GPS, which is not needed, as the Polar 720i records both altitude and distance data). Here are a couple of rides with decent climbs (for me):

employees.org1093736043.04576.srd.htmlOpen ↗
employees.org1083519822.05970.srd.htmlOpen ↗
employees.org1081011138.13435.srd.htmlOpen ↗

There's nothing like being a tri-geek! 🙂

Berend