Audio Doppler Calculate Distance?

I don't think you can without more information.

MY guess is that the minimum amount of information required would be:

1. Velocity of aircraft

2. Velocity and vector of the balloon

3. Audio sample and some form of relative time stamp for that audio.

4. The doppler audio sample would require a sample of the aircraft approaching as well as receding from the balloon with relative time stamps.

5. Ambient atmospheric pressure and humidity is needed to calculate the speed of sound.

6. Lastly, the velocities and vectors for the aircraft and balloon would both be assumed to be constant throughout out the sample period.

The volume of the audio is probably useless because you do not know the absolute sound pressure level nor do you know the sound pressure level the jet makes at some standard distance. There are other complications as well.

Given that much information you could make an estimate. The accuracy would be limited to ability to discriminate both time and frequency.

The long and short of it is, from the simple data you have there you would not be able to get a reliable answer. You may be able to get a rough estimate if you make assumptions about velocities and vectors for balloon and aircraft, but you would be guessing and there are probably better things you will want to do with your time anyway. ;-)

My estimation is that the jet wasn't very close if it didn't motivate the photographer to get a shot of it.

AH is correct that it's not easy to do. Too many variables.

I was wondering if it was unmanned?

I agree that, with comparative acoustic signatures you can do this, but it's still not absolute.

Once worked here: ACTIVE NOISE AND VIBRATION TECHNOLOGIES INC. AND SRI INTERNATIONAL

years ago, and used to characterize many sounds, from automobiles to tanks to Beech Starships and jets.

It would have been even more interesting if the frequency went from maximum to minimum within a fraction of a second...

or after passing the balloon moved because of the wash.

Usbport's approach makes sense. I would draw his graphs a bit differently, reflecting the left half upward so that there was a continuous curve starting at a higher frequency than the actual characteristic frequency of the plane's noise. As the plane passes the balloon, the curve will turn downward, pass through a point of inflection at the plane's characteristic frequency, and then tail off symmetrically to a lower frequency.

The distance between the asymptotes will be proportional to the plane's speed; the slope of the curve at the point of inflection will be inversely proportional to the closest distance between plane and balloon. If the measurements are good enough, theoretically you can deduce both of these.

If you knew the GPS coordinates and the time and date the footage was taken from the balloon you may be able to use Flightaware.com to figure out which flight passed by, then use those coordinates from the flight plan to determine the distance. I know it's not the answer you are looking for, but since you cannot calculate it with the limited data given, it may be a way to make an educated approximation of the distance.

My first impression about this was that it wasn't possible but after having a think I believe it wouldn't be as difficult as first thought.

Lets have a look at the variables:

• Jet's Velocity: This you definitely need to know as the cruising speed can vary drastically from aircraft to aircraft. However, when jets fly in high traffic areas they often stick to a single speed so they don't have problems with faster aircraft running into the back of slower aircraft. In Australia jets tend to cruise at Mach 0.81 so that would probably be a good starting point.
• Velocity & Vector of Balloon: This isn't as complicated as it sounds. The reason being is that all the calculation need to be done with respect to the air and if you take out the vertical component which here wouldn't affect the calculation the velocity of the balloon in the air will be zero.
• Atmospheric Conditions: This is definitely going to cause problems as the speed of sound varies with the density of the air which is effected by the altitude, temperature and humidity, all of which are unknown. However, if we assume the International Standard Atmosphere against which the aircraft's altimeter and Mach meter are calculated we can say that the humidity is 0%, and the ground level pressure is 1013.25 hPa and temperature is 15°C. However, commercial jet aircraft operate most efficiently at specific atmospheric conditions and we can probably assume that the altitude would be somewhere between FL300 (30,000 feet) and FL350 (35,000 feet).

There is however one thing that could throw a huge spanner in the works. We are all assuming that the balloon and aircraft are at the same altitude, if they aren't which is almost certain then you would need to take into account the variation in the atmosphere's density between the two altitudes.

So, if we make a whole stack of assumptions and extracted the timing and frequencies from the video's sound track, which I don't have the kit to do so somebody else may be able to help, then you could probably come up with a minimum and maximum distance at the closest point.

As the jet approaches from far away, the doppler shift will be maximum positive. As it recedes in the distance, it will be maximum negative. Using this difference, calculate the speed. As it passes by, the distance vector will be at an angle to the jet's path. At +/-30 degrees from closest approach, the doppler shift should be half of the maximum value. Using the time between these points and the jet's speed, you can calculate the distance (d=v*sqrt(3)/((t2-t1)*2) of closest approach.

Could you elaborate on how you came up with that equation?

OK. Consider two points on the jet's path at + and - 30 degrees to the closest point of approach (CPA), which makes an equilateral triangle with the perpendicular distance to the CPA sqrt(3)/2 times the side distance. This side distance is the velocity times time.... I stand corrected, the time should be in the numerator. (Sorry about that). So it should be:

d=(t2-t1)*v*sqrt(3)/2. (Does this look right?)

Thanks, MASU

How do you know when the jet is ±30° from the balloon?

Got it. Sin of 30° = .5.

I am disappointed. All this talk about the speed and distance of the aircraft, and nobody posted any results!

So here are the results of my calculations. I will post details about them later:

Airspeed = 503MPH - astonishingly close to cruise speed for most airliners

Distance = 0.1 mile, or 160 meters! Wow!

I must say this was a lot of fun. Now, let me go estimate the airspeed and distance of other moving craft.

Rixter,

A simple dimensional analysis tells me your equation is wrong.

"d" has units of distance. "v/(t2-t1)" has units of distance per time squared.

You would need to *multiply* "v" and "(t2-t1)" just to get the units right.