Odometer Take Vertical Climb Into Consideration?

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I brought my 60CS with me on a mountain bike ride today. Does the odometer take vertical ascent into consideration? Here's an extreme example. If one were to ride one mile up a 45% incline, horizontal travel would only be 1/2 mile. Does the GPS show 1/2 mile on the odomter, or does it actually show the full 1 mile?

Being that you took your GPS with you, I would have thought you would have that answer.

My guess is actual distance is measured. The trails I've gone on measured correctly against the books in spite of the elevation gains.

Edited by TotemLake
Does the odometer take vertical ascent into consideration? Here's an extreme example. If one were to ride one mile up a 45% incline, horizontal travel would only be 1/2 mile. Does the GPS show 1/2 mile on the odomter, or does it actually show the full 1 mile?

The quick answer is that GPS receivers deliberately report horizontal distance covered over ground. So if you parachute straight down one mile the distance would be reported as 0.

However, your math is a bit off in the example you cite. Even if you were able to ride up a 45% grade (keeping the front wheel on the ground becomes rather challenging), the effect on distance travelled isn't all that great. A 45% grade means that for every 1000 horizontal feet moved you gain 450' in altitude. The slope distance you actually travel is then just under 1097' (C^2 = A^2 + B^2), or less than 10% greater than the horizontal distance.

Perhaps you meant a 45° slope, but even then the slope distance would only be 1414' for every 1000' of horizontal distance. And more importantly, at 45° slopes no one would be riding up. For reasonable grades that people ride or walk up the difference between slope and horizontal distance is generally pretty small.

TotemLake - If I'm questioning on whether or not the GPS accurately includes vertical ascent in the distance covered, what good would having my GPS do? I didn't bring my 5,260 foot tape measure with me, so I wasn't able to measure out a mile on the fireroad I was riding on.

Edited by royta

Interesting question. My first inclination would be to tie a string to it and lower it out the window of a tall building, then reel it back in. See if the odometer thinks it went anywhere, or stayed in one spot

If one were to ride one mile up a 45% incline, horizontal travel would only be 1/2 mile.

<Jamie dons his geometry and trigonometry professor glasses>

Did you say 45% or 45°? Your math (although wrong) seems to indicate you mean 45°. Nonetheless, I can address both.

Up a 45° incline, one mile of travel would cover 0.707 horizontal miles, not 0.5mi. You'd have to have a 60° incline for one mile of climbing to equal 0.5mi horizontal.

A gradient of 45% is the same as about 24°. In this case, going one mile up a 24° incline would give you 0.91mi of horizontal travel.

As you can see, the differences when climbing a hill are not nearly so great as you first thought.

<Jamie takes off his professor glasses and puts on spandex cycling shorts and a helmet>

There is no way you can ride up either a 45° or 45% hill. Consider this. From this site, the hills in the Tour de France are defined by five categories. Category 4 is the easiest, and Hors Category is beyond category, or the most difficult:

• Typically for the Tour, Category 4 is an easy, short climb.
• Category 3 is the easiest "real" climb - ie, 5km at a 5% grade.
• Category 2 is about as tough as you could ever see here in the states. (Something like 5km at a grade of 8-8.5%)
• Category 1 typically a long climb (15 - 20+ km) at a not too steep grade - 5-6%.
• Hors Category is long and steep. The altitude difference is at least 1000km and an average grade of 7% or more.

That means that the toughest climbs in the Tour de France is around 8% grade, which is an angle of about 4.6°. At this angle, riding one mile up the hill is 0.997 miles horizontally.

<Jamie now wears a warm cardigan sweater used for consoling>

So.. the long answer to your question is that first you're perceiving much, much greater angles than actually exist. This is very common human error.

Second, using trigonometry, it can be shown that at angles typically encountered on Earth, the actual distance does not differ much from horizontal difference.

And lastly, no... your GPS only sees horizontal movement, so even if it made any difference (such as a freefall in skydiving), the GPS does not know it's moving vertically.

Jamie

 peter beat me.

Edited by Jamie Z
Does the odometer take vertical ascent into consideration?  Here's an extreme example.  If one were to ride one mile up a 45% incline, horizontal travel would only be 1/2 mile.  Does the GPS show 1/2 mile on the odomter, or does it actually show the full 1 mile?

The quick answer is that GPS receivers deliberately report horizontal distance covered over ground. So if you parachute straight down one mile the distance would be reported as 0.

However, your math is a bit off in the example you cite. Even if you were able to ride up a 45% grade (keeping the front wheel on the ground becomes rather challenging), the effect on distance travelled isn't all that great. A 45% grade means that for every 1000 horizontal feet moved you gain 450' in altitude. The slope distance you actually travel is then just under 1097' (C^2 = A^2 + B^2), or less than 10% greater than the horizontal distance.

Perhaps you meant a 45° slope, but even then the slope distance would only be 1414' for every 1000' of horizontal distance. And more importantly, at 45° slopes no one would be riding up. For reasonable grades that people ride or walk up the difference between slope and horizontal distance is generally pretty small.

Geez peter, you quoted my original post for crying out loud. The key words are "extreme example". Of course nobody is going to actually ride a bicycle up a 45 degree slope. But, the example gets a point across for illustrative purposes. You are right though, I did mean a 45 degree angle, not a 45% grade.

I'm trying to use my GPS to set my riding computer to be as accurate as possible. However, I ride on uneven terrain. I guess I need to find a flat road and ride several miles down it.

Ahh c'mon guys! Now Jamie Z is taking my "extreme example" literally.

The steepest section of the climb across .5 mile horizontally, was 12% (11.8%). Vertical climb was 311 feet in .5 miles. I realized how out of shape I was on that little stretch. There were spots in that .5 miles that were steeper than that, but it all averaged to 12%.

Edited by royta
Ahh c'mon guys! Now Jamie Z is taking my "extreme example" literally.

That's what I do. I'm an engineer (wannabee).

Jamie

Thank you Jamie!

I was about to launch into a Trig lesson, but you laid it out fairly well.

(Though I tend to carry it out further to .707107) LOL

Edited by weakfish
Geez peter, you quoted my original post for crying out loud. The key words are "extreme example". Of course nobody is going to actually ride a bicycle up a 45 degree slope. But, the example gets a point across for illustrative purposes. You are right though, I did mean a 45 degree angle, not a 45% grade.

I'm trying to use my GPS to set my riding computer to be as accurate as possible. However, I ride on uneven terrain. I guess I need to find a flat road and ride several miles down it.

It shouldn't be surprising that my post quoted your original post since at the time that I made it that was the only post you had made in this thread. And you seem to have missed the fact that even if you meant 45° rather than 45% you still got the math wrong. To travel one mile and only have a horizontal distance of 0.5 miles would require a slope angle of 60° or a grade of 173%. At that point you'd be using climbing ropes rather than wheels.

As for calibration of your cyclometer, I'd suggest first that a simpler and more accurate method would be to use the roadway marker signs put up by the state tansportation departments. Here in California on country roads they include mileages marked to hundredths of miles measured from the next county line and I've seen similar markers in many other states.

Quicker still and just as accurate is to measure a rollout of your wheel to get the accurate circumference. Put a dab of ink on the wheel, sit on the seat, and roll the bike at least a few revolutions. Measure the distance between marks with a tape measure and use this (usually in cm or mm) as the calibration number for your cyclometer. This should make it considerably more accurate than a GPS odometer.

But if you still insist on using the GPS for calibration then the flatness of the road is likely to be the least source of error. Even if you used the steepest main hiking trail out of the Grand Canyon (the Kaibab), the error due to the vertical rise would only amount to 1% - not a big deal. So you'd really have to go out of your way to find a road with enough slope to cause a problem with your measurement. Far more important would be to pick one without any significant sources of multipath reflections or obstructions of portions of the sky.

Yeah, yeah peter, quit being so critical. What I meant by quoting me, is that you quoted text that I was hoping would let people know that it was an extreme example to get a point across. Oh well, I guess I messed that one up. And no, I'm not a trig major.

Yes, I know how to measure the rolling circumfrence of my tire and enter it into my computer. I'm just a little over the edge when it comes to getting things perfect. When I first started riding in 1993, my friend and I went on a ride through a rather large ranch in the area. We ended up on the highway on the other side and had to ride about 25 miles of highway home. I took that oppurtunity to fine tune the tire circumfrence setting on my computer (Avocet 30 at the time) against the mile markers on the road. Surprisingly, the mile markers were the exact same distance apart. I would have assumed there were not, since Caltrans put them in. Of course, I don't know if they were exactly a mile apart or not, but I felt satisfied that my computer was as spot on as it could be. Anyway, since I'm not a big fan of road riding, I was hoping I could use my GPS to fine tune my Avocet 45 while riding the trails or climbing fire roads.

Edited by royta
Hors Category is long and steep. The altitude difference is at least 1000km and an average grade of 7% or more.

Wow, that is impressive! Almost into medium earth orbit without oxygen.

Peter (whose knee is still a bit sore after riding up some grades of only 21% yesterday, but whose GPS odometer still agreed with the regular cyclometers of the other riders within the normal range of errors)

Edited by peter
Peter (whose knee is still a bit sore after riding up some grades of only 21% yesterday, but whose GPS odometer still agreed with the regular cyclometers of the other riders within the normal range of errors)

Wow, I thought I was doing good with the short 12% burst on my climb today. Of course, I'm just getting serious about riding again after pretty much taking the last 6 years off. I can't wait to get my legs back!

Jamie Z is correct on the trig stuff.

If you have a science calculator, put in the angle of the climb (45) then hit the COS key. It will come with a factor of .707. You will notice that if you do a 5 percent climb, the factor is .996 or about 22 feet per mile climbed. So if the climb isn't that harsh, the GPS isn't going to be off that much.

But if you are going to do some mountain climbing, the GPS meausring your distance traveled will be inaccurate unless you know the angle of the climb or decent.

In other words, if you know the climb is 45 degrees, take your GPS odometer reading and DIVIDE it by .707 to find the true distance walked. So if the GPS says you walked 2 miles but you know you climbed at 45 degrees... take the 2 miles divide it by .707 which means you actually walked 2.82 miles total.

To the bike rider who climbed up to 21 degrees, if you did your entire ride at a 21 climb or decent, the COS of 21 degree is 0.93 which would mean you would be off only 7 percent max. Since you probably only averaged a few degrees climbing or decent for your entire ride, the difference between an cyclometer and a GPS isn't going to be that noticable.

Edited by gpsblake

I think the errors inherent in the GPS will probably be greater than the trigonometric variations of distance you're worrying about!

One would never use a standard off the shelf GPSr for accurately determining the actual distance travelled!

If you need this much precision, you'd be needing a 50cm accurate survey grade instrument!

To the bike rider who climbed up to 21 degrees, if you did your entire ride at a 21 climb or decent, the COS of 21 degree is 0.93 which would mean you would be off only 7 percent max.

No one in this thread claimed to ride up a 21° grade. I indicated that portions of my ride were at a 21% grade which is considerably less steep (11.9°) and would result in the slope distance being 2.2% more than the horizontal distance for that portion of the ride. Naturally it ends up being totally negligible over the whole ride distance, most of which was on flatter terrain.

Yes, but if another rider was coming down 4.2 miles/hour faster than your rate of travel, and their mass was only 75% of yours, what color bike shorts would they be wearing?

Yes, but if another rider was coming down 4.2 miles/hour faster than your rate of travel, and their mass was only 75% of yours, what color bike shorts would they be wearing?

Black, duh.

TotemLake - If I'm questioning on whether or not the GPS accurately includes vertical ascent in the distance covered, what good would having my GPS do? I didn't bring my 5,260 foot tape measure with me, so I wasn't able to measure out a mile on the fireroad I was riding on.

But if you knew the marked distance you wouldn't need the tape. However, be that as it may, you must've missed the winkie which meant I was jesting with ya.

there is a pretty cheap way to test this. get a cheap Bicycle computer and Accurately adjust it to give accurate results (equal to your gps on level ground)

go riding. the bicycle computer will give actualy rolling distance. compare this to the GPS after enough distance to remove spurrious errors

Chris Taylor

http://www.nerys.com/

Over the rides I've compared, the two have generally been very close. When the GPS has been longer, almost invariably there is a stray point or two in the track which throws the distance off. When the GPS shows a shorter distance, there's often not much correlation to the amount of climbing. I think that some kinds of things like riding in tight circles waiting for my friends probably doesn't register as distance to the GPS, but does to the cyclocomputer. With these and other factors, it's going to be very hard to figure out how much contribution the vertical climb is making to any net discrepancy. It probably would have been a bit easier when I lived near the mountains in California where I could do a ride that was nearly all climbing. In the rolling terrain where I live now, I don't see that happening.

Keith

No GPS unit that I know of includes the vertical in the distance calculation. It's pretty negligible anyway; even for a quite steep hill (20% grade), it would only change the distance traveled by less than 2%.

In fact, here's a plot of how much further it is as a function of the grade of a hill. A 20% grade is steep on foot, let alone a bicycle!

From a tracklog, you could actually do the calculation and see what the difference would be quantitatively. GPS odometers are notoriously inaccurate because of their sampling algorithm. Tracklogs are usually better.

Here is the profile of a 40 mile Ultramarathon I plan to do in February:

If you look at the horizontal profile of this image, it's 37 miles and change. The other 3 or so miles are the hypotenuse of the triangle.

I'm carrying a gps with me on the race anyways. I think I'm going to use the glide-path feature to help me compute progress.

- T of TandS

Five thousand two hundred.....and what?

Actually I find the OP's original question quite interesting. I have, for reasons not known at this time, never thought about this. I have always thought that the GPSr was calculating the distance traveled over the earth's surface even if you are sitting in an airliner seat. So it seems to me that since the GPSr detects direction, speed of travel and changes in altitude that it contains the information needed to calculate actual distance traveled. Whether or not GPSr's actually perform these calculations, I certainly do not know.

I suppose that the crux of the question is, does the GPSr calculate 'horizontal' travel only?

I think that I'll fire off a question to Magellan wrt this. God only knows if they will ever respond.

Edited to reflect peter's response. Thank you peter.

Edited by Team Cotati
Unfortunately in reading thru the posts I cannot determine if there has been an answer supplied. Strange that.

You might try again; my initial post, Jamie's, and Fizzy's all gave explicit answers to the original question.

Unfortunately in reading thru the posts I cannot determine if there has been an answer supplied. Strange that.

You might try again; my initial post, Jamie's, and Fizzy's all gave explicit answers to the original question.

Thank you. Just as I expected.

Edited by Team Cotati

Tands---

Doing it the theoretical way,on thecomputer in Topo......

In the example profile you gave, the "3705" is the distance "On the Ground" including elevation changes. (ie odometer reading)

If you knew your exact starting waypoint coordinates and your ending coordinates then you can easily calculate the actual straight line ,point to point distance. Use UTM coordinates, it's easier.

Since you have Topo, you can do it there easily like you did the profile. Use the "compass" tool and place the "anchor" on the starting waypoint, then go to the end waypoint and click, and the length of the direction line is your straight line distance. (In "Preferences" have "feet" selected for distance choice)

As has been previously suggested, you will be surprised how small the diference actually is, especially in real world "travel conditions".

In Topo I constructed a sample direction line between two waypoints 2748 ft apart, and checked the profile. The line went straight over the top of a nearby "fourteener" and the % average grade (in Topo) showed to be 80%+. On ground distance showed to be 3578 ft...so 830 ft difference due to the extreme incline example conditions.

Save the starting point and ending point on your ultra run, come back and download it into Topo and you can definitively answer your own question for all of us, by seeing which distance your GPSr odometer most closely agrees with.

Grasscatcher,

This is not my plot. This is generated by a track from the race organizers' gps. The distance 'on the ground of this race is 40 miles, measured by walking rolling odometer. Most of the course is on parts of old trading trails and railroad bed. These parts, additionally, have the distance surveyed. In this race, the mechanically measured and surveyed distance is 40 miles. Yet the horizontal distance of the race as seen from space as gps sats see it is 37 miles as measured by GPS. In this case, the distance of the race missed by the satellites is in fact about 3 miles, or approximately 7.5% which is hardly small.

If you hiked the AT, much much longer than 40 miles, the discrepancy would balloon to dozens of miles.

- T of TandS

Edited by tands

In a local forest where we train the elevation fluctuates several hundred feet many times over a ten mile distance. My GPS regularly measures the IMBA certified trail distances short by about .75 miles per 10 miles of trail.

- T of TandS

But... that discrepancy on my local trails is the odometer. I need to check the tracklogs, doh! However, the race course I posted really does have the boner discrepancy concerning GPS distance vs actual distance.

- T of TandS

However the TOPO vertical profile seems to be doing a virtual integral on the track, and the total vertical rise+descent adds up to approximately the missing 3 miles.

Unfortunately most folks don't have the laptop with them on the trail.

- T of TandS

However the TOPO vertical profile seems to be doing a virtual integral on the track, and the total vertical rise+descent adds up to approximately the missing 3 miles.

Unfortunately, you can't just add rise and descent to the horizontal distance to get the total distance. The effect of the rise and descent is very much smaller than that. Pythagorean theorem and all that.

I don't know why they claim that the race is 40 miles, because, according to your data, it's nowhere near that. If it's 37 miles horizontally, I would guess the actual distance is maybe 37.3 miles.

According to GPS captured data, but with all the ups and downs the race is 40. Measured over ground mechanically. Don't know why you didn't read that....

My point is that, in my experience, on terrain with a lot of vertical in it, up and down, GPSR distance over ground accuracy is variable and unreliable. Point to point distance is great, but when you get the woop-de-doos in there it is a Kahuna-Biter.

Plenty familiar with geometry, BTW. But you're assuming a straight hypontenuse, on trails, the rise or fall is usually a curve, not a straight line, so standard trig doesn't apply, but calculus, with integrals describing curved lines and space, does.

And finally, a big fan of FizzyMagic

- T of TandS

Edited by tands
My point is that, in my experience, on terrain with a lot of vertical in it, up and down, GPSR distance over ground accuracy is variable and unreliable.

But you appear to be assuming that any discrepancy is due to the horizontal vs. slope measurement difference. That's hardly the case since there are numerous other possible measurement difficulties. In the type of terrain you're describing GPS reception is frequently rather marginal reducing accuracy and maybe even including short sections where the GPS loses lock temporarily and dead-reckons for awhile. In addition the trails are probably rather twisty so the intermittent position sampling done by a GPS can round off some of the corners further reducing the distance it measures. OTOH, a rolling-wheel measuring device operated on rough ground can somewhat overestimate distances since it goes up and over little rocks, roots, and other obstructions on the path that the hiker/runner will naturally step over without covering any extra distance.

Together, those types of errors can lead to the discrepancy that you're observing even if the horizontal vs. slope issue didn't exist.

Sure, a calculation of the actual slope distance would require a line integral over the exact profile of the course, but we can get some idea of the reasonableness of the numbers by considering simple slopes. To get an error of 7.5% would require a grade of almost 40%. Glancing at your race course profile, it isn't credible to me that the grades would be anywhere near steep enough to generate that large an error. It's certainly a difficult course, and I'm glad I won't be on it (best of luck BTW!), but I agree with FizzyMagic that the slope vs. horizontal error would be a few tenths of miles rather than 3 full miles.

According to GPS captured data, but with all the ups and downs the race is 40.  Measured over ground mechanically.  Don't know why you didn't read that....

My point is that, in my experience, on terrain with a lot of vertical in it, up and down, GPSR distance over ground accuracy is variable and unreliable.  Point to point distance is great, but when you get the woop-de-doos in there it is a Kahuna-Biter.

Sorry. I wasn't clear before. I am claiming that it is not the up-and-down that causes the difference in distances. The difference in distances you see over rougher terrain is only indirectly caused by the vertical component.

Mechnical distance measurement has its own set of problems, especially on a course like that one. My guess is that it is the little twists and turns of the trail, rather than the up and down, that makes the difference.

Both distance and elevation measurements are fractal, so it's hard to define either in a way that makes sense for the kind of terrain in question here. It's like the famous question about the length of the California coastline: at a suitably large scale, it looks to be about 900 miles long, but at a small enough scale it becomes effectively infinite. The length of the coastline depends on the scale of the measurements.

It's exactly the same thing here. The mechanical and GPS distance measurement use different scales, so it is not surprising that you get different answers. I believe that the reason you see more of a difference in rougher terrain is not a result of the additional distance from the up-and-down, but rather that paths in rougher terrain tend to be crooked on a scale of the order of tens of feet. The GPS odometer probably measures distances with an average scale of a couple of hundred feet. So you would expect the mechanical distance measure to be longer. It's hard to say which one is "better," because it depends on what you are comparing the distance to.

I ran into this problem when I was writing AnalzeTrack, which takes a tracklog and calculates the total vertical gain and loss. Just adding together all the ups and downs gives a number that is remarkably large. Because of the way it is added, that method adds any noise coherently. So if the elevation reported by your GPS has any noise in it, all the noisy ups and downs get added to the gain and loss totals, even though they are not real. My solution there was to tune a parameter that estimates the noise in the GPS elevation and ignore any elevation fluctuations below the threshold. Seems to work pretty well.

I didn't mean at all to imply that you didn't understand basic trig! Sorry about that. I was only trying to claim that it is not the up and down per se that is responsible for the differences you are seeing.

One more comment about the Topo profile. ..If you had Topo and placed your cursor on the end point of the profile and looked just above the taskbar on the left hand side just below the 37.05, It would say "Terrain Distance(includes ups and downs" 37.05.

Also one more comment about the "walking rolling odometer"(notoriously inaccurate) and "mechanically measured and surveyed"distance. If that profile is from the starting line to the finish line of the exact course that you will be running , then you will be running a 37.05 mile course. Enjoy your shortened race, or run an extra 2.95 mile so that you can calculate an accurate pace /mile.

I've run 7 marathons, all "measured and certified", several of which were later shown to be inaccurate distances. The point?, relax and enjoy the run, because the sun will still come up the next day whether you win or place last.

I've always wondered about a related question with regard to surveys and legal descriptions. If one looks at surveyed sections, say one mile squares, from space, they are all one mile squares, and this is regardless of the ups and downs. It is as if the measured distance by the surveyor of one mile were projected into space. in fact, the squares are not horizontally equal. they are up and down equal. an acre is an acre even if it is on the side of a hill

Just want to finish! And there can be many many reasons why GPS odometers read the wrong distance, but the fact is, they do read wrong most often in my experience on trails. I spend 15 hours per week or more running trails, and multiple GPSRs read the distance short. I accept the distance inaccuracy could be caused by things other than elevation change, but it's the most obvious culprit to me, even if I'm wrong...

- T of TandS

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