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Can we determine the speed of an aircraft...

Skepticalone
Posts: 6,095
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9/21/2016 2:27:33 AM
Posted: 2 months ago
...from the ground?

This is a question for some of you mathy types. ;-)

We can see the plane moving across the sky and let's say we know its altitude, can we figure out its speed? If not, what else do we need?
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keithprosser
Posts: 1,968
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9/21/2016 6:47:17 AM
Posted: 2 months ago
The maths is easy.... Making the measurents, (altitude, distance and track) is hard. Just keep the cross hairs a tad in front and let the IR homing system do the rest.
dee-em
Posts: 6,464
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9/21/2016 6:51:50 AM
Posted: 2 months ago
At 9/21/2016 2:27:33 AM, Skepticalone wrote:
...from the ground?

This is a question for some of you mathy types. ;-)

We can see the plane moving across the sky and let's say we know its altitude, can we figure out its speed? If not, what else do we need?

I think you can but you would need to be directly under the path of the plane or it gets complicated. You would also need a clock and some way to measure the angle from you to the plane. You measure the angle once and use simple trigonometery of right-angled triangles to get the distance from you to the plane (sine) since you know the altitude. Then wait for a fixed interval (depends on altitude - the higher up the plane is the longer you can wait) and then measure the angle again getting the distance to the plane again. You now have two sides of a triangle (the third being the distance the plane has travelled) and you can calculate the angle between them from the other two angle measurements. Again, knowing two sides and the angle between them (side-angle-side or SAS) will allow you to calculate the third side (the distance travelled) using the cosine rule. The speed is then distance travelled over elapsed time.

The measurement won't be exact because the plane is flying a slightly curved path to maintain a constant altitude relative to the Earth's surface, but close enough.
dee-em
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9/21/2016 6:57:30 AM
Posted: 2 months ago
To make it easier, you could make one of the measurements be when the plane is directly overhead. The angle is then 90 degrees and the distance from you to the plane is simply the altitude. That should speed up the overall calculation.
Skepticalone
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9/21/2016 12:30:53 PM
Posted: 2 months ago
At 9/21/2016 6:51:50 AM, dee-em wrote:
At 9/21/2016 2:27:33 AM, Skepticalone wrote:
...from the ground?

This is a question for some of you mathy types. ;-)

We can see the plane moving across the sky and let's say we know its altitude, can we figure out its speed? If not, what else do we need?

I think you can but you would need to be directly under the path of the plane or it gets complicated. You would also need a clock and some way to measure the angle from you to the plane. You measure the angle once and use simple trigonometery of right-angled triangles to get the distance from you to the plane (sine) since you know the altitude. Then wait for a fixed interval (depends on altitude - the higher up the plane is the longer you can wait) and then measure the angle again getting the distance to the plane again. You now have two sides of a triangle (the third being the distance the plane has travelled) and you can calculate the angle between them from the other two angle measurements. Again, knowing two sides and the angle between them (side-angle-side or SAS) will allow you to calculate the third side (the distance travelled) using the cosine rule. The speed is then distance travelled over elapsed time.

The measurement won't be exact because the plane is flying a slightly curved path to maintain a constant altitude relative to the Earth's surface, but close enough.

Interesting. It seems similar to measurements we take of some stars 6 months apart. ..parallax?

I should have said I only have a video of the aircraft. Any thoughts on that?
This thread is like eavesdropping on a conversation in a mental asylum. - Bulproof

You can call your invisible friends whatever you like. - Desmac

What the hell kind of coked up sideshow has this thread turned into. - Casten
Ramshutu
Posts: 4,063
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9/21/2016 1:40:34 PM
Posted: 2 months ago
At 9/21/2016 2:27:33 AM, Skepticalone wrote:
...from the ground?

This is a question for some of you mathy types. ;-)

We can see the plane moving across the sky and let's say we know its altitude, can we figure out its speed? If not, what else do we need?

If you have an observer underneath the plane, and a second observer a known distance away measuring the visible angle of the plain; you can calculate the height. If the height remains constant, all you need then is a second measurement of angle a known amount of time later.

You can do it with a sextant a stop watch and a map.

I have all three :D
Ramshutu
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9/21/2016 1:42:14 PM
Posted: 2 months ago
At 9/21/2016 1:40:34 PM, Ramshutu wrote:
At 9/21/2016 2:27:33 AM, Skepticalone wrote:
...from the ground?

This is a question for some of you mathy types. ;-)

We can see the plane moving across the sky and let's say we know its altitude, can we figure out its speed? If not, what else do we need?

If you have an observer underneath the plane, and a second observer a known distance away measuring the visible angle of the plain; you can calculate the height. If the height remains constant, all you need then is a second measurement of angle a known amount of time later.

You can do it with a sextant a stop watch and a map.

I have all three :D

But no second friend to assist with the measurement :(

http://i0.kym-cdn.com...
Skepticalone
Posts: 6,095
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9/21/2016 1:56:14 PM
Posted: 2 months ago
At 9/21/2016 1:42:14 PM, Ramshutu wrote:
At 9/21/2016 1:40:34 PM, Ramshutu wrote:
At 9/21/2016 2:27:33 AM, Skepticalone wrote:
...from the ground?

This is a question for some of you mathy types. ;-)

We can see the plane moving across the sky and let's say we know its altitude, can we figure out its speed? If not, what else do we need?

If you have an observer underneath the plane, and a second observer a known distance away measuring the visible angle of the plain; you can calculate the height. If the height remains constant, all you need then is a second measurement of angle a known amount of time later.

You can do it with a sextant a stop watch and a map.

I have all three :D

But no second friend to assist with the measurement :(

http://i0.kym-cdn.com...

Lol, Ram

https://cdn.meme.am...
This thread is like eavesdropping on a conversation in a mental asylum. - Bulproof

You can call your invisible friends whatever you like. - Desmac

What the hell kind of coked up sideshow has this thread turned into. - Casten
keithprosser
Posts: 1,968
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9/21/2016 4:44:03 PM
Posted: 2 months ago
If the plane is flying directly towards or away the angular difference would be tiny. As I said earlier, the calc is trivial, the measurements ridiculously hard. In practice forget sextants and maps.... Get a Doppler enabled radar like they have at airports.
Skepticalone
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9/21/2016 5:01:52 PM
Posted: 2 months ago
At 9/21/2016 4:44:03 PM, keithprosser wrote:
If the plane is flying directly towards or away the angular difference would be tiny. As I said earlier, the calc is trivial, the measurements ridiculously hard. In practice forget sextants and maps.... Get a Doppler enabled radar like they have at airports.

Lol, that doesn't tell how to do it! Plus, I think the Doppler enabled radar is probably out of reach financially... at least for most people.
This thread is like eavesdropping on a conversation in a mental asylum. - Bulproof

You can call your invisible friends whatever you like. - Desmac

What the hell kind of coked up sideshow has this thread turned into. - Casten
Ramshutu
Posts: 4,063
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9/21/2016 5:20:39 PM
Posted: 2 months ago
At 9/21/2016 4:44:03 PM, keithprosser wrote:
If the plane is flying directly towards or away the angular difference would be tiny. As I said earlier, the calc is trivial, the measurements ridiculously hard. In practice forget sextants and maps.... Get a Doppler enabled radar like they have at airports.

If a plane is traveling overhead; the angular difference in 20 seconds will be large and measurable.

If you have a second observer making the same measurement of angle from, say, 500 meters away; the angular difference will also be large and measurable.

A sextant or even a protractor can be used to make a rough estimation of the angles, and then calculate the speed.
dee-em
Posts: 6,464
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9/21/2016 11:43:25 PM
Posted: 2 months ago
At 9/21/2016 12:30:53 PM, Skepticalone wrote:
At 9/21/2016 6:51:50 AM, dee-em wrote:
At 9/21/2016 2:27:33 AM, Skepticalone wrote:
...from the ground?

This is a question for some of you mathy types. ;-)

We can see the plane moving across the sky and let's say we know its altitude, can we figure out its speed? If not, what else do we need?

I think you can but you would need to be directly under the path of the plane or it gets complicated. You would also need a clock and some way to measure the angle from you to the plane. You measure the angle once and use simple trigonometery of right-angled triangles to get the distance from you to the plane (sine) since you know the altitude. Then wait for a fixed interval (depends on altitude - the higher up the plane is the longer you can wait) and then measure the angle again getting the distance to the plane again. You now have two sides of a triangle (the third being the distance the plane has travelled) and you can calculate the angle between them from the other two angle measurements. Again, knowing two sides and the angle between them (side-angle-side or SAS) will allow you to calculate the third side (the distance travelled) using the cosine rule. The speed is then distance travelled over elapsed time.

The measurement won't be exact because the plane is flying a slightly curved path to maintain a constant altitude relative to the Earth's surface, but close enough.

Interesting. It seems similar to measurements we take of some stars 6 months apart. ..parallax?

Yes, except there they use angle-side-angle (ASA) on an isoceles triangle and the sine rule.

I should have said I only have a video of the aircraft. Any thoughts on that?

Hmmm. Not really.
Ramshutu
Posts: 4,063
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9/22/2016 12:22:27 AM
Posted: 2 months ago
At 9/21/2016 12:30:53 PM, Skepticalone wrote:
At 9/21/2016 6:51:50 AM, dee-em wrote:
At 9/21/2016 2:27:33 AM, Skepticalone wrote:
...from the ground?

This is a question for some of you mathy types. ;-)

We can see the plane moving across the sky and let's say we know its altitude, can we figure out its speed? If not, what else do we need?

I think you can but you would need to be directly under the path of the plane or it gets complicated. You would also need a clock and some way to measure the angle from you to the plane. You measure the angle once and use simple trigonometery of right-angled triangles to get the distance from you to the plane (sine) since you know the altitude. Then wait for a fixed interval (depends on altitude - the higher up the plane is the longer you can wait) and then measure the angle again getting the distance to the plane again. You now have two sides of a triangle (the third being the distance the plane has travelled) and you can calculate the angle between them from the other two angle measurements. Again, knowing two sides and the angle between them (side-angle-side or SAS) will allow you to calculate the third side (the distance travelled) using the cosine rule. The speed is then distance travelled over elapsed time.

The measurement won't be exact because the plane is flying a slightly curved path to maintain a constant altitude relative to the Earth's surface, but close enough.

Interesting. It seems similar to measurements we take of some stars 6 months apart. ..parallax?

I should have said I only have a video of the aircraft. Any thoughts on that?

Do you have a frame of reference, and do you know what type of plane it is?
keithprosser
Posts: 1,968
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9/22/2016 2:24:01 AM
Posted: 2 months ago
If it's a fairly good video, I'd try to work out 'plane lengths per frame' and get mph from that.
chui
Posts: 507
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9/22/2016 7:41:21 AM
Posted: 2 months ago
At 9/21/2016 2:27:33 AM, Skepticalone wrote:
...from the ground?

This is a question for some of you mathy types. ;-)

We can see the plane moving across the sky and let's say we know its altitude, can we figure out its speed? If not, what else do we need?

Identify the plane, google the cruising speed, job done.
dee-em
Posts: 6,464
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9/22/2016 11:59:55 AM
Posted: 2 months ago
At 9/22/2016 7:41:21 AM, chui wrote:
At 9/21/2016 2:27:33 AM, Skepticalone wrote:
...from the ground?

This is a question for some of you mathy types. ;-)

We can see the plane moving across the sky and let's say we know its altitude, can we figure out its speed? If not, what else do we need?

Identify the plane, google the cruising speed, job done.

That's not a mathy answer, but good lateral thinking. :-)
chui
Posts: 507
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9/22/2016 12:32:05 PM
Posted: 2 months ago
At 9/22/2016 11:59:55 AM, dee-em wrote:
At 9/22/2016 7:41:21 AM, chui wrote:
At 9/21/2016 2:27:33 AM, Skepticalone wrote:
...from the ground?

This is a question for some of you mathy types. ;-)

We can see the plane moving across the sky and let's say we know its altitude, can we figure out its speed? If not, what else do we need?

Identify the plane, google the cruising speed, job done.

That's not a mathy answer, but good lateral thinking. :-)

True, but the problem, as initially stated, is a pretty easy bit of trig as you have pointed out above. So I was being deliberately flippant.
Looncall
Posts: 451
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9/22/2016 8:50:25 PM
Posted: 2 months ago
At 9/21/2016 2:27:33 AM, Skepticalone wrote:
...from the ground?

This is a question for some of you mathy types. ;-)

We can see the plane moving across the sky and let's say we know its altitude, can we figure out its speed? If not, what else do we need?

This reminds me of one of my favourite stories.

A student was asked how to measure the height of a building using a barometer.

He answered that one could drop it from the roof and time its fall, or compare the length of its shadow with the length of the building's shadow, or approach the building's owner and say "I will give you this fine barometer if you will tell me the height of your building.".
The metaphysicist has no laboratory.