What Is The Speed?

[cabinetman]

A friend of mine was on a commercial flight and thought it would be cool to check flight data on his portable GPS. He said that the speed indicated didn't come close to what the pilot announced.

As we talked about it, there seems to be different speeds relevant to some reference point. If the GPS is tracking movement, is it some reference point on the ground, and not actual air speed? Would the data change in relation to the planes' positioning to a certain satellite?

So, we kind of made a comparison of a table saw blade on the arbor. If you drew a straight line from the arbor to one of the teeth, and turned on the saw, there is a difference in speed with relation to a reference point. The tip speed (RPM) would be a whole lot greater than the arbor speed (RPM).

Getting back to the aircraft and the GPS, how is the airspeed figured?
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[x00018]

Airspeed

A GPS measures ground speed just like a speedometer in your car. The captain gave airspeed. To get the ground speed you need to add or subtract to effect of the wind speed on the aircraft. If the plane is going 500 mph airspeed into a 100 mph headwind the ground speed would be 400 mph.

[dkerfoot]

I had started to answer with my understanding of it (which was mostly right), and then found this website by someone who can explain it much better than I:
http://www.aerospaceweb.org/question...ts/q0210.shtml

[crokett]

This is a good question and thanks for the link explaining it. Now I have a question... my wife's GPS lists MPH. On the drive home from Indy it was consistently about 2MPM slower than what the speedometer on the van registers. So which is more accurate? The van or the GPS? I'd think the van, except if I put larger/smaller tires on it, I can change what the speedometer registers while the GPS is unaffected by this.

[LCHIEN]

RPM is angular velocity (as opposed to linear velocity) and is the same on a moving axis no matter where its measured. So the arbor and blade tips all have the same RPM.
Linear velocity can be the sum of the instantaneous vector components in which case the tip velocity is constant, approx 100 mph. or it can be broken into the vector components, forwards and downwards (we'll omit sideways for a blade discussion) in which case each one will actually change in a sine pattern with respect to time, e.g. 100mph forwards slowing to minus 100 mph forwards (as it traverses the bottom). At the same time the downwards or vertical vector component is also oscillating back and forth from +100 to -100. If you recall your high school geometry the square root of the sum of the squares of the vertical and horizontal vectors will be a constant (e.g. 100 mph) and the plot of vert and horz vectors over time describes a circle (surprise).

Back to the plane, the pilot's basic instrument package gives the airspeed which is how fast the plane is moving with regards to the air. THis is measure with a pitot tube which measures differential pressure into the mouth of a forward pointing tub compared to the atmospheric pressure. A GPS receiver is a LOCATION device that basically locates coordinates on the planet. By repeated taking locations over a fixed interval of time, and comparing them, it can discern North, East and vertical velocity components and computer the absolute velocity, as well as computer the direction of travel. All relative to points on the ground - so it gives true speed over the ground. Now the pilot does have navigational instruments incorporating location receivers, notably GPS, but they historically report speed as airspeed unless otherwise qualified.

I think the in-cabin navigational displays show ground speed. When I took my GPS receivers with me in the past they usually indicated well; inclduing altitude. But post 9/11, I was stopped in France at the screening and told in no uncertain terms I could not take my GPS in the cabin baggage. I ended up checking my briefcase with the GPS in it. Nonetheless I stopped carrying GPS for a while. I do now ocassionally but most airlines if you read the list prohibit operating GPS in the cabin. Besides the most interesting use is in tracking the approach to the airport doing turns and circles and dropping altitude... all airlines require turning off personal electronics during this phase. I admit I have kept mine on sometimes...

Crockett, I would tend to trust the GPS more.
The car can have several percent based on just how round the tires are and how the car is loaded... a quarter inch of the tire flattening under a load is a big part of the 20" or so total wheel radius. I have clocked several cars and find as much as 3-4 mph off at 60 mph, the worst was 6 mph off (guy probably had the wrong tires).
OTOH, GPS timing is incredably accurate and the differential positioning over a short time period is very, very accurate, much more accurate than the absolute positioning accuracy. Only differential positioning info is used for speed calculations. I have been working with GPS systems on and off since 1987.

[cabinetman]

RPM is radial velocity (as opposed to linear velocity) and is the same on a moving axis no matter where its measured. So the arbor and blade tips all have the same RPM.

Loring, I don't quite agree with this rationale, but I may be wrong in theory. Looking at the end of the arbor, with a saw blade mounted, draw a line from the center of the arbor to one of the teeth. Granted, the arbor has rpm, but my reference is to speed of the tip of the blade to me would have a greater speed than the edge of the line where it strikes the outer edge of the arbor.

CASE IN POINT: Lets take a track and field event where runners are competing on a track comprised of lanes being circles. For just this point I'll use even numbers. The first lane is a 40' diameter circle (the outer line of the lane). The last lane is a 200' diameter circle (the outer line of the lane). Now just to demonstrate my theory, if there is a runner in the first lane (@40') and one in the last lane (@200'), in order for the two runners to circle the track and maintain an imaginary straight radii (like the big hand of an analog clock), the runner in the last lane has to run much faster than the one in the first lane.
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[Alex Franke]

Looking at the end of the arbor, with a saw blade mounted, draw a line from the center of the arbor to one of the teeth. Granted, the arbor has rpm, but my reference is to speed of the tip of the blade to me would have a greater speed than the edge of the line where it strikes the outer edge of the arbor.

I think Loring is just pointing out the difference between RPMs and linear velocity. There's no doubt that the edge of the blade is covering more distance over the same amount of time as the inside of the blade, but no matter how big the blade is, the edge always rotates around the center point the same number of times per minute as a point much closer to the center.

[430752]

Car's speedo made to be in error

Now I have a question... my wife's GPS lists MPH. On the drive home from Indy it was consistently about 2MPM slower than what the speedometer on the van registers. So which is more accurate? The van or the GPS? I'd think the van, except if I put larger/smaller tires on it, I can change what the speedometer registers while the GPS is unaffected by this.

For the longest time MFR's have been fudging the speedos to read quicker than actually are going, usually starting at about 30mph and increasing thereafter. E.g. 31 might acutally be 30, 55 might acutally be 53 and 75 might actually be 72. I think it was done for the proverbial "best interests of the public" and "safety" issues. My wife's honda pilot at highway speeds (70-80) reads 3mph over actual (magellan) gps speeds. My ,merc reads 2mph over actual at highway speeds. So yes, big brother is out there, falsifying inputs to you to affect your behavior.

[Bigbit]

Loring, I don't quite agree with this rationale, but I may be wrong in theory. Looking at the end of the arbor, with a saw blade mounted, draw a line from the center of the arbor to one of the teeth. Granted, the arbor has rpm, but my reference is to speed of the tip of the blade to me would have a greater speed than the edge of the line where it strikes the outer edge of the arbor.

CASE IN POINT: Lets take a track and field event where runners are competing on a track comprised of lanes being circles. For just this point I'll use even numbers. The first lane is a 40' diameter circle (the outer line of the lane). The last lane is a 200' diameter circle (the outer line of the lane). Now just to demonstrate my theory, if there is a runner in the first lane (@40') and one in the last lane (@200'), in order for the two runners to circle the track and maintain an imaginary straight radii (like the big hand of an analog clock), the runner in the last lane has to run much faster than the one in the first lane.
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Cabinetman: Loring is correct in his description. You are confusing rotational speed (how many rotations per unit time) with surface speed. Surface speed is rotational speed X distance from point of rotation (circumference). So you are correct with your track analogy, but only due to the fact that the outer ring of the track covers a greater distance.

To get you thinking further on this, imagine you are located at the equator of the earth. The rotational speed of the earth is 1 rev per day or 1/1440 rpm. The surface speed at the equator, since the approximate circumference of the earth is 40075 km, is 27.83 km/m (40075/1440). At either of the poles, rotational speed is the same, 1/1440 rpm or 1 rpd. It's surface speed, however, is 0 km/m, since the distance from point of rotation is 0. In other words, at the two poles of the earth, surface speed is exactly 0.

[LCHIEN]

Loring, I don't quite agree with this rationale, but I may be wrong in theory. Looking at the end of the arbor, with a saw blade mounted, draw a line from the center of the arbor to one of the teeth. Granted, the arbor has rpm, but my reference is to speed of the tip of the blade to me would have a greater speed than the edge of the line where it strikes the outer edge of the arbor.

CASE IN POINT: Lets take a track and field event where runners are competing on a track comprised of lanes being circles. For just this point I'll use even numbers. The first lane is a 40' diameter circle (the outer line of the lane). The last lane is a 200' diameter circle (the outer line of the lane). Now just to demonstrate my theory, if there is a runner in the first lane (@40') and one in the last lane (@200'), in order for the two runners to circle the track and maintain an imaginary straight radii (like the big hand of an analog clock), the runner in the last lane has to run much faster than the one in the first lane.
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Excuse me, I said radial velocity when I should have said angular velocity (corrected the original post). Angular velocity is always the same whether on the arbor or the blade tip. Angular velocity is given in RPM, Degrees/second, radians per second, cycles per second, where 1 cycle=360 degrees=2xPi radians=1 revolutions.

I stand by my statement as correct in ref to angular velocity.

[cabinetman]

Excuse me, I said radial velocity when I should have said angular velocity (corrected the original post). Angular velocity is always the same whether on the arbor or the blade tip. Angular velocity is given in RPM, Degrees/second, radians per second, cycles per second, where 1 cycle=360 degrees=2xPi radians=1 revolutions.

I stand by my statement as correct in ref to angular velocity.

Thanks for clearing that up.
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[wbsettle]

For the longest time MFR's have been fudging the speedos to read quicker than actually are going, usually starting at about 30mph and increasing thereafter. E.g. 31 might acutally be 30, 55 might acutally be 53 and 75 might actually be 72. I think it was done for the proverbial "best interests of the public" and "safety" issues. My wife's honda pilot at highway speeds (70-80) reads 3mph over actual (magellan) gps speeds. My ,merc reads 2mph over actual at highway speeds. So yes, big brother is out there, falsifying inputs to you to affect your behavior.

I don't think there's a "conspiracy" here. Air pressure, treadwear, and manufacturing/mechanical tolerances could easily induce more offset than you're seeing. The tolerances in the tires, wheels, speedo cable, etc. are cumulative to the final result and I seriously doubt any of them are spec'd better than 1%.

My 2K3 4Runner was overstating speed by 1-2 mph near the end of the original tire's treadlife. New tires and the speedo and GPS are dead on from 0 - 70+ within my degree of accuracy in reading the speedo (parallax, bouncing eyeballs, etc.). Our 2k6 CR-V seems to be similarly accurate when I've bothered to check.

-Brent

[ragswl4]

Great discussion. Makes me think that the automakers should dump the old methods of computing speed and use GPS. There are many new vehicles with GPS built in anyway.

[master53yoda]

RPM verses FPM for pulleys etc.

RPM = revelations per minute this does not very whether your talking about a 1/2" shaft or a 15' fan blade.

FPM = Feet per minute and is calculated by taking the RPM x the circumference of the circle The larger the circle the faster the FPM is at the same RPM

changing speeds on a drill press etc is based on the motor pulley diameter at fixed speed RPM and varying the pulley size gives the belt a FPM speed and transfers the power to the other pulley divided by the circumference of the driven pulley giving the RPM of the driven shaft.

if it is desired I can provide formulas for pulley calcs.

[drumpriest]

There is a definite amount of error introduced by measuring speed via GPS as well, it is proportional to the sample rate. The GPS is measuring velocity by using a summation approximation of an integral, and therefore error occurs.

Do I win any nit-picky awards?? Either method gives close enough results in a car, but which is more accurate depends upon which accumulated error is greater, which would be interesting to measure using a fixed track length and monitoring the 2. Seems like something the mythbusters would have fun doing.