Downhill speed

[Geek Boy]

When travelling downhill, (ie skiing, snowboarding, cycling) is your speed measured relative to the slope or according to the horizontal?

 

I've just ordered an eTrex Legend and haven't been able to try this for myself. Not so much a concern on my bike since I have a speedometer but it would be interesting to know how fast I'm going on a snowboard.

 

Thanks!

[+culpc]

I would guess that the speed is relative to the slope, not the horizontal since it get the same speed reading in the car when I go down a long hill as when I'm on flat ground. If the reading was to the horizontal I would expect to see a speed reduction since some of my forward motion is now downhill...

 

Fat, drunk, and stupid is no way to go through life, son!

[+culpc]

I would guess that the speed is relative to the slope, not the horizontal since it get the same speed reading in the car when I go down a long hill as when I'm on flat ground. If the reading was to the horizontal I would expect to see a speed reduction since some of my forward motion is now downhill...

 

Fat, drunk, and stupid is no way to go through life, son!

[+Jamie Z]

As far as I know, the speed indicated on the GPS is horizontal only.

 

Chaz... the reason your car speedometer reads the same as the GPS going down a hill is this...

 

On a 6% grade, the difference between the speedometer and GPS would be only 0.2%. That is, if you are traveling up a hill at 60mph, your GPS will read 59.9mph. Not enough difference to notice.

 

Now... if you were freefalling, your velocity may well be over 100mph, but your GPS will read zero, unless you have some lateral movement.

 

Jamie

[+Alan2]

quote:

---

Originally posted by Jamie Z:

Now... if you were freefalling, your velocity may well be over 100mph, but your GPS will read zero, unless you have some lateral movement.

 

Jamie

---

 

A time you'd wish you left you Garmin home and brought a parachute!

 

Alan

[+Alan2]

quote:

---

Originally posted by Jamie Z:

Now... if you were freefalling, your velocity may well be over 100mph, but your GPS will read zero, unless you have some lateral movement.

 

Jamie

---

 

A time you'd wish you left you Garmin home and brought a parachute!

 

Alan

[Geek Boy]

I'm only speculating but since the receiver is aware of elevation changes, wouldn't it be able to calculate the change in distance both vertically and horizontally over time to determine velocity?

 

Seems like a pretty simple calculation.

 

(sqrt(v^2 + h^2))/time = velocity

[+mrp]

quote:

---

Originally posted by Geek Boy:

I'm only speculating but since the receiver is aware of elevation changes, wouldn't it be able to calculate the change in distance both vertically and horizontally over time to determine velocity?

---

 

The calculation is trivial compared to all the other math it's doing (solving multiple nonlinear simultaneous equations of intersecting 4 dimensional parabolic hyperboloids) However, in almost all practical cases the difference in speed is trivial, and since vertical dilution of position (vertical error) is relatively high, and delta_h can fluctuate quite wildly, putting it in would lead to a much larger error in speed calculations that just leaving it out. Even on a relatively steep ski slope (20%), the difference would only be 10% or so.

 

If you're hurtling down the ski slope, you may be interested in the vertical speed readout.

 

-- Mitch

[peter]

quote:

---

Originally posted by Pneumatic:

However, in almost all practical cases the difference in speed is trivial, and since vertical dilution of position (vertical error) is relatively high, and delta_h can fluctuate quite wildly, putting it in would lead to a much larger error in speed calculations that just leaving it out. Even on a relatively steep ski slope (20%), the difference would only be 10% or so.

---

 

I agree with the first part, but you're still exagerating the effect. On a 20% ski slope the difference between slope speed and horizontal speed is less than 2%.

[+Lil Devil]

quote:

---

Originally posted by Pneumatic:

If you're hurtling down the ski slope, you may be interested in the vertical speed readout.

---

 

I think you'd be more interested in watching the terrain in front of you instead of your GPSr. A Garmin up your nose is gonna hurt when you do a face plant.

 

Lil Devil

[vstanescu]

quote:

---

Originally posted by Jamie Z:

Chaz... the reason your car speedometer reads the same as the GPS going down a hill is this...

---

 

The car measures the speed using wheel rotation. The wheels are rotating the same number of times on a given distance, and the fact that this distance is covered climbing a hill, descending a slope or going straight has no relevance for the measurement method. It is just the distance along which you are going.

 

The GPS might (or might not - I don't know about this) calculate the speed between two coordinates using only lat&long. If it uses the height also (calculating the distance between the 3D coordinates) it will give the speed that the car is showing.

[vstanescu]

quote:

---

Originally posted by Jamie Z:

Chaz... the reason your car speedometer reads the same as the GPS going down a hill is this...

---

 

The car measures the speed using wheel rotation. The wheels are rotating the same number of times on a given distance, and the fact that this distance is covered climbing a hill, descending a slope or going straight has no relevance for the measurement method. It is just the distance along which you are going.

 

The GPS might (or might not - I don't know about this) calculate the speed between two coordinates using only lat&long. If it uses the height also (calculating the distance between the 3D coordinates) it will give the speed that the car is showing.

[+mrp]

quote:

---

Originally posted by peter:

I agree with the first part, but you're still exagerating the effect. On a 20% ski slope the difference between slope speed and horizontal speed is less than 2%.

---

 

You're quite right. I had a brain fart when I made up those numbers and did sqrt(1.2) instead of sqrt(1+(0.2^2)).

 

quote:

---

Originally posted by vstanescu:

The car measures the speed using wheel rotation. The wheels are rotating the same number of times on a given distance, and the fact that this distance is covered climbing a hill, descending a slope or going straight has no relevance for the measurement method. It is just the distance along which you are going.

 

The GPS might (or might not - I don't know about this) calculate the speed between two coordinates using only lat&long. If it uses the height also (calculating the distance between the 3D coordinates) it will give the speed that the car is showing.

---

 

Thanks for being patronizing and wrong at the same time. The speed your spedometer gives can be wrong for a whole lot of reasons, most notablely that they're usually poorly calibrated at best (+/- 10%, or roughly 5mph at highway speeds), and the fact that even if precisely calibrated, they're highly suceptible to issues like tire size/inflation and slippage.

 

Now, lets say you're on the maximum slope allowed on major roads, roughtly 10%. That means that you descend (or rise) 10 ft for every 100 ft that you go horizontally. (This is pretty steep. most highways have a maximum incline of 6 or 7%) For a a 10% grade, for every 100 ft horizontally you would actually travel sqrt(100^2 + 10^2) ft, or roughtly 100.5 ft, or less than 1/2 of a percent difference, which is paltry compared to the 10% error that most spedometers already have.

 

Now most GPSRs claim a +/- 0.5 mph accuracy, or roughtly 1% error at highway speeds. The difference between measuring horizontal and "true" distance is already below the accuracy threshold, and anybody who would drive 50 mph down a 10% slope is a ballsier man than I.

 

Now, lets say the GPSR tried to use vertical displacement. Most GPSRS are far less accurate in the vertical plane than in the horizontal, which means that vertical position may vary by up to 50-100 ft in subsequent readings. Since a typical leg legth of a track is 40-60 ft, this means that occasionally the GPSR will see a slope of 100-200%, and will show speeds that are 40-75% too high, drastically REDUCING the accuracy of the measurements.

 

Of course, if you skiing down a 200% hill (pretty extreme even for expert skiers), your speed measurements will only be 58% of what they should be, but then you should use the tracklog and calculate the average yourself. This is a small price to pay for great accuracy in "normal" situations. If you're sky-diving, then you probably want 100's ft/min or ft/sec anyway, and most GPSRs have one of those as an option.

 

-- Mitch

[+mrp]

quote:

---

Originally posted by peter:

I agree with the first part, but you're still exagerating the effect. On a 20% ski slope the difference between slope speed and horizontal speed is less than 2%.

---

 

You're quite right. I had a brain fart when I made up those numbers and did sqrt(1.2) instead of sqrt(1+(0.2^2)).

 

quote:

---

Originally posted by vstanescu:

The car measures the speed using wheel rotation. The wheels are rotating the same number of times on a given distance, and the fact that this distance is covered climbing a hill, descending a slope or going straight has no relevance for the measurement method. It is just the distance along which you are going.

 

The GPS might (or might not - I don't know about this) calculate the speed between two coordinates using only lat&long. If it uses the height also (calculating the distance between the 3D coordinates) it will give the speed that the car is showing.

---

 

Thanks for being patronizing and wrong at the same time. The speed your spedometer gives can be wrong for a whole lot of reasons, most notablely that they're usually poorly calibrated at best (+/- 10%, or roughly 5mph at highway speeds), and the fact that even if precisely calibrated, they're highly suceptible to issues like tire size/inflation and slippage.

 

Now, lets say you're on the maximum slope allowed on major roads, roughtly 10%. That means that you descend (or rise) 10 ft for every 100 ft that you go horizontally. (This is pretty steep. most highways have a maximum incline of 6 or 7%) For a a 10% grade, for every 100 ft horizontally you would actually travel sqrt(100^2 + 10^2) ft, or roughtly 100.5 ft, or less than 1/2 of a percent difference, which is paltry compared to the 10% error that most spedometers already have.

 

Now most GPSRs claim a +/- 0.5 mph accuracy, or roughtly 1% error at highway speeds. The difference between measuring horizontal and "true" distance is already below the accuracy threshold, and anybody who would drive 50 mph down a 10% slope is a ballsier man than I.

 

Now, lets say the GPSR tried to use vertical displacement. Most GPSRS are far less accurate in the vertical plane than in the horizontal, which means that vertical position may vary by up to 50-100 ft in subsequent readings. Since a typical leg legth of a track is 40-60 ft, this means that occasionally the GPSR will see a slope of 100-200%, and will show speeds that are 40-75% too high, drastically REDUCING the accuracy of the measurements.

 

Of course, if you skiing down a 200% hill (pretty extreme even for expert skiers), your speed measurements will only be 58% of what they should be, but then you should use the tracklog and calculate the average yourself. This is a small price to pay for great accuracy in "normal" situations. If you're sky-diving, then you probably want 100's ft/min or ft/sec anyway, and most GPSRs have one of those as an option.

 

-- Mitch

[+Jamie Z]

Thanks Mitch.

 

Jamie

[+culpc]

Perhpas we could shoot someone's (not necessarily mine) GPS up with in a model rocket to test the downhill arguments. I guess that a skydiver would serve the same purpose.

 

This could lead to a new sport-Aerocaching!

 

Fat, drunk, and stupid is no way to go through life, son!

[+culpc]

Perhpas we could shoot someone's (not necessarily mine) GPS up with in a model rocket to test the downhill arguments. I guess that a skydiver would serve the same purpose.

 

This could lead to a new sport-Aerocaching!

 

Fat, drunk, and stupid is no way to go through life, son!

[+apersson850]

In revision 2.28 of the Vista firmware, they've included the ability to display glide ratios, like 50:1, if you are going 50 meters horizontally, for every meter down (or feet or whatever, since it's just a ratio). So, on a 10% slope, it would show you 10:1. I haven't tried that yet, well, not while checking the glide ratio, that is.

 

But Mitch, driving 50 mph (that's just 80 km/h) down a 10% slope is really nothing, is it? On the other hand, I'm not using an American car...

 

Anders

[+apersson850]

In revision 2.28 of the Vista firmware, they've included the ability to display glide ratios, like 50:1, if you are going 50 meters horizontally, for every meter down (or feet or whatever, since it's just a ratio). So, on a 10% slope, it would show you 10:1. I haven't tried that yet, well, not while checking the glide ratio, that is.

 

But Mitch, driving 50 mph (that's just 80 km/h) down a 10% slope is really nothing, is it? On the other hand, I'm not using an American car...

 

Anders

[+Gliderguy]

I hope they come out with a firmware for the Garmin V that includes the glide ratio.

 

As a glider pilot that would be very useful info to have (as head/tail winds and or sinking air can greatly effect useful glide ratio in a glider)

[+apersson850]

quote:

---

Originally posted by Gliderguy:

I hope they come out with a firmware for the Garmin V that includes the glide ratio.

---

 

It can tell you the glide ratio you have (it's reduced to _____:1 if you climb) and the glide ratio you ought to have to come to your destination (I haven't really tried this, but I assume you have to set a waypoint, with altitude specified, so it has something to aim to).

It can also tell you your vertical speed towards the destination, not measured as a glide ratio, but in meters/minute (or m/s or ft/min).

 

Since the GPS V doesn't have any barometric altimeter, I assume you can wish for that functionality until you get blue in your face.

Time to complement your gear with a Vista, perhaps?

 

Anders

[+apersson850]

quote:

---

Originally posted by Gliderguy:

I hope they come out with a firmware for the Garmin V that includes the glide ratio.

---

 

It can tell you the glide ratio you have (it's reduced to _____:1 if you climb) and the glide ratio you ought to have to come to your destination (I haven't really tried this, but I assume you have to set a waypoint, with altitude specified, so it has something to aim to).

It can also tell you your vertical speed towards the destination, not measured as a glide ratio, but in meters/minute (or m/s or ft/min).

 

Since the GPS V doesn't have any barometric altimeter, I assume you can wish for that functionality until you get blue in your face.

Time to complement your gear with a Vista, perhaps?

 

Anders