# Can Doppler Shift be used to calculate speed of an observed object?

Thanks for looking. Just musing over an idea this afternoon: if I had a radio controlled plane, I could obviously calculate its airspeed based on pings and the known speed of sound if it was traveling on a straight path away or towards me.

Now lets say I need to get it's ground speed if it was traveling a line perpendicular to my viewpoint. Here, measuring scheduled pings won't reveal the correct speed because if the plane was flying in a perfect circle with me at the circle's center the speed would appear to be zero since the distance or ping response has no deviation.

Ok, so what about doppler shift? I think some of my brain came out of my ear when trying to picture how that would work in a perfect circle with me at it's center, so let's keep it simple and visualize the straight path that is perpendicular to where my view point (flying left to right or right to left in my viewable area).

Assuming I had a radio control that could receive some sort of pings from the RC aircraft, could I use Doppler Shift to calculate the aircraft's airspeed?

# Bonus!

What type of sensor could interpret the relative "bunching" of sound waves that we know as Doppler Shift? (Yes, obviously I want to know the ground speed of my RC airplane. I know this is possible with GPS, but I am a software engineer so naturally I make things more complicated than they need be!)

**Disclaimer: I am not a physicist, I am a software engineer. Apologies in advance if I have asked a dumb question that made Newton (or Doppler in this case) spin in his grave!

• This is how police radar work. Many sonar systems use it to. – mmesser314 Apr 3 '16 at 21:56
• Thanks @mmesser314 but can that really apply to my use case? With police radar, the observer is in a stationary spot and basically "shooting" measurements against an approaching object that stays on a generally linear course; So two "shots" give them a reliable calculation of speed because it is assumed that the object in question is travelling a consistent linear path. Am I missing something? – Matt Cashatt Apr 3 '16 at 22:00
• @mmesser314-Also to clarify (since I may not be articulating my question properly), please imagine the perfect circle scenario with me at the circle's center and the airplane flying the circle around me. In that scenario, wouldn't the speed always be zero mph? – Matt Cashatt Apr 3 '16 at 22:05
• Doppler shift can only show speed towards or away from you. If the plane is flying in a circle around you, you will not get any Doppler effect. – hdhondt Apr 3 '16 at 23:49
• @hdhondt Not true. The (relativistic) transverse doppler effect is small, but real. – Rob Jeffries Apr 4 '16 at 13:05

If you are at the centre of a circular motion, then the shift can be attributable to the time dilation experienced by the plane and the observed frequency is decreased by a factor $(1-v^2/c^2)^{1/2}$.
The more general expression would be $$f = \frac{f_0 (1-v^2/c^2)^{1/2}}{1 + (v/c)\cos\theta},$$ where $\theta$ is the angle that the velocity of the source makes (in the reference frame of the observer) with the line between source and observer ($\theta <\pi/2$ means the source is getting further away).
As has been pointed out in comments below, this is obviously a very small effect when dealing with non-relativistic velocities. Whilst the principle doppler effect is of order $v/c$, the transverse doppler effect is of order $v^2/c^2$. Hopefuly you will get further comments or answers on how you could feasibly do this for a RC aircraft using some alternate technique (I think the effect is just too small for any detection technology available), but the above is what the doppler effect can tell you (which is what you asked).