Inspired by the smart phone sensor discussion I got to thinking about measuring speed. I’m using the term “speed” instead of “velocity” to simplify things since vehicles don’t necessarily travel in a constant straight line. Do the common methods we use to indicate speed actually measure the speed directly?
Take the most basic way to measure speed. If we know the distance from one point to another we can measure the time it takes to travel this distance. A simple calculation gives average speed. But note we measured time and calculated speed.
LIDAR gets a lot of recognition these days. How does it measure up? It pulses a LED which sends out a beam of light. When that light hits an object and travels back to the LIDAR gun it measures the elapsed time. So it measures time and converts to distance. Then it repeats the sequence many times. I used to work with one of NASA’s laser experts and he was often called as an expert witness in trials to explain the problems with LIDAR. I forget the actual specs but the gun takes like 50 readings in 20 milliseconds (microseconds?) and plots them. Then it fits a best straight line to the data and the slope of the line is speed. So LIDAR measures time, converts to distance repeatedly and calculates speed from that.
How about RADAR? It sends out a microwave pulse and when it encounters an object it bounces back to the unit. The flight time can convert to distance but the unit does not use that data for speed indication. Instead it measures the shift in frequency of the returned pulse and a calculation provides speed. So does the shifted frequency directly measure speed? I don’t know.
Every vehicle has a speedometer and the most basic principal is well known. A flexible cable is driven by a gear in the drive train and runs into the back of the speedometer on the instrument panel. On the end of the cable is a bar magnet that spins with the cable. The magnet is inside, but not touching, a metal drum. The faster the magnet spins the more rotational torque it induces on the drum. The drum has a small spiral spring attached and the drum rotates until the magnetic spin torque is matched by the spring. A needle on the front of the drum indicates speed on the speedometer dial. I think that is a direct measurement of speed.
Hmmm. A more interesting question than it at first appears. Puts me in a mind of this deceptively interesting question:
Certain forms of RADAR and LIDAR work on the Doppler principle. Send a pulse and listen to how the reflection’s frequency is perceived. Not time of flight. If you know your reflecting background is stationary, the resulting frequency shift is proportional to speed. Actually wavelength shift, but the idea is the same. But again that’s a calculation of speed, not a direct discovery of speed. In a sense your RADAR lays out a standing wave pattern in front of you that you then drive over, counting the peaks and valleys per unit time. Which is no different than a car computing its speed by counting the rate at which the fixed-size lane stripes go by.
Some older radars do (did) derive speed from delta position over time, not using Doppler.
Your primitive pre-electronic auto speedometer example isn’t measuring speed at all. It’s measuring the RPM of the driveline and performing a RPM → meter torque → needle position translation using your coil AKA voltmeter movement. That’s an analog computer if you will. I’m not sure that’s a direct measurement of anything.
But the conversion from needle position to vehicle speed is provided by the calibration process that painted the e.g. “60mph” mark at a particular spot on the dial, and your eyeball to compare the moving needle to the fixed background. And that calibration assumes X rpm at the driveline converts to Y feet/second of vehicle motion. Which depends on built-in assumptions about tire diameter, differential ratio, etc. And of course any imprecision in the electromechanical parts.
Let’s go back to definitions, and again deliberately overlooking the difference between speed and velocity. Or equivalently, considering only the 1D vector case.
Speed is defined as d-position / dt. Speed is strictly meaningless as dt actually gets to zero, rather than simply as dt → 0 as a limit. So you can’t measure it in the same static sense that you can hold a ruler up to an object and determine its length. Non-zero time is an inherent component of speed. As dimensional analysis also suggests.
So perhaps we’re stuck with measuring a position, measuring a time and performing that division. Whether numerically, via an analog mechanism, or whatever, we’re still performing dpos/dt over a non-zero time interval dt.
What is “speed”, as distinguished from “velocity”?
Because the definition of velocity tells you everything you need to know: \Delta d\over \Delta t (the change in distance or position divided by the change in time).
So you can only determine velocity by measuring spatial displacement and elapsed time. There is no “directly measuring speed”.
Just to muddy the water a bit. The YouTube channel Veritasium has an interesting video (below) that claims no one has measured the speed of light. That seems obviously not true. The trick here is no one has measured it in one direction. You have to include a return trip and, mathematically, that return trip could be instantaneous and the math still works (or any combination that adds up to light speed).
I don’t think he is seriously claiming that’s how the world works but the thing is, we can’t prove it.
As I noted in the earlier thread, GPS isn’t a great way to measure speed. You can log the raw satellite inputs and post process these into a very good estimate of speed, but getting an instantaneous measure is hard, and most units I know of use Doppler from the satellites. Which is not as accurate, but provides as useful a measure as is attainable with a timely update.
All measurement techniques you can come up with suffer from the same families of errors. A basic problem is the noise floor and bandwidth of the measurement system.
If you measure the time it takes for a wheel to make a rotation there is an implicit low pass filter placed on the measurement. You can’t see changes in speed of less than a rotation period. A rough road surface adds noise to the measurement as do a whole mess of other factors.
The same things manifest in other methods. Doppler has bandwidth, and estimates are low pass filtered. The bandwidth of the transmitted signal is never zero in the real world. (You need infinite time for that.). So there are intrinsic bounds on accuracy. (One might recognise the same underlying question as Heisenberg here.) Noise creeps in in a fundamental manner to limit accuracy.
Doppler tries to estimate speed from the frequency of the shift from the transmitted signal. In a simple system this can be the frequency of the low pass filtered hyderodyne product of the two. That is never a perfect single frequency. Same issue. Accuracy improves with time. In the limit of zero time, accuracy is non-existent. You cannot estimate the frequency of something in zero time.
Much of the above is just the duality of temporal versus frequency spaces. And the lack of free lunches. You can cover most of the ground with corollaries to Shannon and information theory, especially including the Nyquist Shannon sampling theorem.
Well, if we’re starting with the premise that it’s possible to measure distance directly, what does it mean to measure distance? I measure distance by putting a meterstick down next to the thing I want to measure. What’s a meterstick? Basically, it’s a standard object that’s 1 cm long, and a standard object that’s 2 cm long, and so on, up to one that’s 100 cm long. In the specific case of a meterstick, all of these 100 standard objects are combined into a single object for convenience, but that’s not actually necessary: I could, instead, use a set of 100 different unmarked rods.
To measure speed directly, then, I would have a standard set of objects, each moving at a different speed. And I would then compare my unknown object in turn to the 1 m/s object, and to the 2 m/s object, and to the 3 m/s object, and so on. It would of course be more difficult to maintain these speed standards than a length standard, but it could in principle be done.
I think a car’s speed could easily be measured with a barometer. Place a barometer a known distance from some designated starting point on the road. Attach a string to the barometer that spans the roadway about a foot and a half over the road surface. Tie another string to the barometer and attach it at the other end to a hammer hinged to a wooden base and delicately balanced so that even a gentle tug on the string will cause the hammer to fall forward with the peen striking a small clock preset at an established time with enough force to stop it. Have the car start at some prior point on the road and reach a steady velocity. Note the time on your watch when the car crosses the designated starting point. When the car drives down the road and runs the string stretched over the roadway the barometer will be pulled toward the road thus causing the hammer to fall and stop the clock. Using math in some way the distance from the starting point and the time on the broken clock, I think the the speed of the vehicle can be determined.
That sound more like converting a measurement of torque into a correlated measure of speed. When the spring starts to wear out, the displayed speed won’t be as accurate.
This common nitpick perpetuated by high school physics teachers doesn’t actually hold water in the wider world. While “speed” is never used for the vector quantity, “velocity” is routinely used to refer to the scalar quantity in both formal and vernacular settings. (It’s also used routinely for the vector quantity as well, of course, just in different contexts.)
I’m not sure I follow the OP. How does one draw a line between a “direct” and “indirect” measurement? I would posit that we don’t measure anything directly, at a sufficient level of pedantry. It feels subjective to me as to whether a specific measurement approach feels direct. But maybe the OP has something concrete in mind as a definition of “direct”.
While I’m all in favor of ginning up interest in science, which this video does, I think it obfuscates what is actually going on. It isn’t that the speed of light might be different in different directions, its that the notion of simultaneity at different points in space is enforced by our physical laws and so we can arbitrary decide what we want to call simultaneous provided that our choice doesn’t violate causality. If we decide to rejigger our space time coordinate system so that every light year we travel in a particular direction we set out clock forward 6 months, physics is cool with that, its just as if the speed of light from that direction was twice as fast. The video makes it sound like the speed of light might actually be fast of slow in one direction and we just didn’t know for sure, when in fact the speed of light in a particular direction is whatever we decide it is (within limits) based on our choice of coordinate systems. Of course the one where it’s the same in all directions is the obvious choice for simplicity.
What is “direct” and what is “measure” in the OP’s mind? In ours? I’d like to see the OP’s idea of examples of physics parameters that can be “directly measured.” Or those they believe cannot be so measured and why.
The quibbles about speed versus velocity are simply failure to read the thread for comprehension.
I think by ‘directly’, the OP is asking how (or if) we can measure the instantaneous speed of an object (i.e. not by measuring the distance it moves over a period of time, but rather, by making a single measurement with no duration to it).
I’m not certain it’s meaningful to be able to do that, even if it were possible (I’m aware of the uncertainty principle BTW)
That is why there are plenty of encoders with 4096 or more pulses per rotation.
Your problem then is not accuracy. It is how much resources do you want to commit to measuring the delta-v of a 2 ton vehicle?
Is anyone interested in the 4th decimal of the speed of their car?
I know there are theoretical problems in measuring speed, but for practical uses those have been solved.
Combined with GPS (to correct for wear of tires or low pressure) it is trivial to measure speed accurately with a sample rate measured in kHz.: that should be enough for most applications.
I also mentioned GPS because after we invested billions, users can now measure their speed (with reasonable accuracy) with a chip costing cents. So for most speed measurements it is a very cost effective tool. Especially because you don’t have to connect it mechanically.
I see. I didn’t read the OP that way originally since, if that’s the OP’s question, he answered his own question in his OP, citing both magnetic speedometers and (with some stated uncertainty) Doppler-based devices as examples of instantaneous measurements. But upon re-reading I do agree with you that that’s likely what the OP is talking about.
In which case the answer to the titular question is of course ‘yes’, and one could construct loads of devices, based on a number of distinct physical principles, to provide a measure of instantaneous velocity.
