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Consider a pod (about 50 ft long and 15 square feet wide) that levitates using air pressure that shoots through the bottom and travels through a tube that's at low air pressure (about 100 Pa). It travels using linear induction. If you're wondering, this problems comes from the hyperloop tube specification. The pod will be traveling anywhere from 0 to 800 MPH.

I need to measure the speed of the pod traveling through the tube at every point

Approaches I have considered:

  1. Using an accelerometer and integrating over time
  2. Using a pitot tube

I've heard that an accelerometer can be bad for measuring velocity because an error bias can propagate.

I heard that pitot tubes were used for airplanes, but I don't know if they're very accurate or work at the low air pressures I have.

What approach should I use to measure the speed of my pod?

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    $\begingroup$ The linear induction system can and almost inevitably will have periodic structures which will allow you to derive very precise location information from the track. I wouldn't worry about this "problem", at all, the folks who will design that part of the system will take care of that for you. $\endgroup$
    – CuriousOne
    Commented Oct 28, 2015 at 1:11
  • $\begingroup$ @CuriousOne The updated hyperloop tube spec says "Every 100 feet, a 2-inch wide reflective circumferential stripe will be applied to the inner circumference of the tube." under the navigation system. Do you think this will suffice for determining the velocity? $\endgroup$
    – michaelsnowden
    Commented Oct 28, 2015 at 1:19
  • $\begingroup$ IMHO, that would be more than enough, but I would say that it's probably just a backup system to much finer resolution readily achieved by the drive mechanism. Don't get me wrong, but the Hyperloop, so far, strikes me still as the product of people who like to sing in the shower but have very little (if any) experience with the design of large systems. This "problem" and its ad-hoc solution in the specification (a document which is NOT supposed to have a fixed solution to the demands that it makes) is one of those little hints that are giving this away. $\endgroup$
    – CuriousOne
    Commented Oct 28, 2015 at 1:23
  • $\begingroup$ It appears that is the least of their problems. $\endgroup$
    – JDługosz
    Commented Sep 13, 2016 at 4:30

3 Answers 3

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Police use the answer all the time: relativistic Doppler effect with radar or lasers. It's very well understood technologically, theoretically, and practically.

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  • $\begingroup$ There is no "relativiy" in polices radar apparatus. $\endgroup$
    – Georg
    Commented Feb 8, 2017 at 12:26
  • $\begingroup$ What do you mean? The Doppler effect on radar and light is a relativistic effect. The radar computer, however, is a superheterodyne transceiver which produces a beat frequency between the transmitted and received wave. The beat frequency is used to calculate the speed of the detected vehicle, and it absolutely must use the relativistic shift equation to calculate the speed. $\endgroup$
    – Bill N
    Commented Feb 9, 2017 at 3:04
  • $\begingroup$ repeating something wrong does not improve anything. Read about "relativity" $\endgroup$
    – Georg
    Commented Feb 14, 2017 at 19:41
  • $\begingroup$ Tell me specifically what's wrong. The Doppler shift equation of EM waves is different from the Doppler shift of sound. That's due to the fixed speed of light in any reference frame. That's special relativity. $\endgroup$
    – Bill N
    Commented Feb 14, 2017 at 20:00
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As you said, "dead-reckoning" using an accelerometer isn't a good method because errors can easily build up. My feeling is that a pitot tube isn't a good method, either, for a number of reasons. For one, there may be big air pressure variations over vehicle's hull as it moves slightly within its tube, and that may cause chaos with the pitot tube readings. It's not quite like using a pitot tube with an airplane with free airflow all around the aircraft.

I think that a simple method to implement which would take advantage of the fact that the hyperloop vehicle is within a close-fitting tube would be to but regular markers of some sort on the tube and some sensor in the vehicle so that the vehicle can 'count' the rate at which the markers on the tube are passing it. Some possible markers would be regularly spaced LED lights on the inside of the tube or even painted stripes on the inside of the tube. The vehicle could then determine its speed using a sort of opto-electric sensor system similar in concept to that used in the optical mouse that you are now using at your computer.

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Mount an optical or laser mouse on the pod, so that it goes along the tube wall. The autocorrelator chip in the mouse will do the brain work for you.

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