Doppler effect - two airplanes flying towards each other

[Ondyman]

Homework Statement

Two airplanes are flying towards each other with the speed of 2 MACH (we do not know the exact speed of each airplane, just "mutual" speed of their movent to each other). We need to find a correct channel spacing to be sure that the communication between these two aircraft will not be interrupted by doppler effect... These two aircraft are able to broadcast between 118 - 136 MHz band. And second question is, if we find a correct channel spacing, how many channels can fit into 118 - 136 MHz band (however, if we can find a spacing, this second task will not be a problem)

Relevant Equations

DOPPLERS FORMULA

I found it confusing since there is only "mutual" speed of both aircrafts and hence I do not know how to correctly put it into the common Dopplers formula...

 

[berkeman]

Homework Statement:: Two airplanes are flying towards each other with the speed of 2 MACH (we do not know the exact speed of each airplane, just "mutual" speed of their movent to each other). We need to find a correct channel spacing to be sure that the communication between these two aircraft will not be interrupted by doppler effect... These two aircraft are able to broadcast between 118 - 136 MHz band. And second question is, if we find a correct channel spacing, how many channels can fit into 118 - 136 MHz band (however, if we can find a spacing, this second task will not be a problem)
Relevant Equations:: DOPPLERS FORMULA

I found it confusing since there is only "mutual" speed of both aircrafts and hence I do not know how to correctly put it into the common Dopplers formula...

What would be your answers if it were just one plane approaching the tower at Mach 2? (and why would those answers be any different if it is two planes approaching each other at a relative Mach 2?)

 

[Ondyman]

allright, thanks!
So if I use a common formula for doppler and set original frequency to 118 MHz, the frequency which tower (or other plane) got is 354 MHz

f=f0*((v+v0)/v)
where f = ?
f0 = 118 MHz
v´ = speed of sound = 343 ms
v0 = speed of airplane towards the tower = 2 MACH = 636 ms
I got the f´ = 354 MHz...

however, now I do not know how to deal with the channel spacing problem... If I transmit signal on frequency 118 MHz and tower receive it at 354 MHz it means, that I can use basically any frequency between 118 - 136 MHz and it will not be affected by interfence. - only IF we fly slower and the frequency of 118 MHz would be shifted by doppler effect to i.e. 119 MHz , it would mean that we cannot use 119 Mhz for transmitting... so we should use the 2 MHz channel spacing.

Nonetheless, It means in our case we can use any frequency between 118 and 136 MHz with standard channel spacing (which is 8,33 or 25 KHz) and our signal will not be affected by interference, right? :)

 

[berkeman]

v´ = speed of sound = 343 ms

Radio communication does not use sound waves...

 

[Ondyman]

God... thank you.. quite tired this afternoon...

f=f0*((v+v0)/v)
where f = ?
f0 = 118 000 000 Hz
v´ = speed of light = 299 000 000 ms
v0 = speed of airplane towards the tower = 2 MACH = 636 ms
f = 118 000 270.7 Hz

it means that the singal will be shifted by 270.7 Hz.. so all we need is to set channel spacing to roughly 300 Hz, and it should work, ok?
That would mean that between 118 and 136 MHz we can put roughly 60 000 frequencies which will have channel spacing 300 Hz (i.e.: first 118 000 000 Hz, second 118 000 300 Hz, third 118 000 600 Hz, ...).

 

[berkeman]

God... thank you.. quite tired this afternoon...

No worries.

it means that the singal will be shifted by 270.7 Hz.. so all we need is to set channel spacing to roughly 300 Hz, and it should work, ok?

The channel spacing is not just based on any potential Doppler shift of the center frequency of each channel. It is also based on the bandwidth of the communication. You can't have 20kHz wide channels spaced only 300Hz apart. The overlapping frequencies would ruin communication.

So start with the bandwidth of the information in each channel (is that given? something like 20kHz voice?), plus some guard bands for the bandpass filters to roll off enough to keep down the cross-channel interference.

You can see an example by looking at how the WiFi and ZigBee channels in the 2.4GHz band are spaced. Look at the channel width (which is based on the data speed needed for each channel), plus some guard band spacing between the channels.

Does the problem tell you what each channel's information bandwidth is plus the required guardbands?

https://www.researchgate.net/publication/327174774/figure/fig1/AS:664591931539457@1535462472996/Channel-distribution-of-different-technologies-in-24GHz-frequency-band.png

 

[Ondyman]

Theory says that in real life in band 118 - 136 MHz we would use 8,33 kHz spacing in civil aviation and 25 kHz spacing in military aviation. However, I think this problem is just made up to see if I can use Dopplers formula... However, if I focus only on Doppler part of this problem, the shift is calculated correctly...? Channel spacing in real life would be probably 8,33 kHz and it means to our band of 118 - 136 MHz we can squeeze roughly 2 220 cahnnels (first 118 MHz, second 118 008 330 Hz, third 118 016 660 Hz,...)

 

[berkeman]

it means that the singal will be shifted by 270.7 Hz

if I focus only on Doppler part of this problem, the shift is calculated correctly...?

I get 251.0Hz instead of your 270.7Hz, so maybe double check the calculation?

Theory says that in real life in band 118 - 136 MHz we would use 8,33 kHz spacing in civil aviation and 25 kHz spacing in military aviation.

Since these planes are doing a combined Mach 2, it sounds like they are military jets, not civilian jets. So I personally would use the military channel spacing, plus the small delta for accommodating the Doppler shift.

 

[Ondyman]

thank you! :)