Airplane landing on a runway

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In summary, the Attempt at a Solution was unable to solve the problem of getting the correct angle for landing. They tried vector addition and found that they had the correct groundspeed, but could not find the angle. They think they must be interpreting something wrong, and need to do a scale drawing to figure out how to turn the angle into a bearing.
  • #1
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Homework Statement


i3HuD.png


The Attempt at a Solution


I tried to use vector addition. I got the correct groundspeed (65.9). However I could not get the angle. The answer key says the angle is 87.7 degrees but I can't see how I can get that with my diagram. I think I must be interpreting something wrong.

http://i.imgur.com/LNscV.jpg
 
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  • #2
Basically you need to sketch out the scalene triangle and work out the interior angles.
Some of them you can get from what you are given, like the angle between the runway and the wind, but I suspect the one you want will need the sine rule or the cosine rule.
Ten you have to convert the interior angle to a bearing.

If you get stuck - try doing a careful scale drawing with a ruler and protractor :)

Note: for a bearing of 87.7 degrees, the plane must be approaching the runway from the opposite side to that shown in the diagram (or fly in backwards!)
 
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  • #3
Simon Bridge said:
Basically you need to sketch out the scalene triangle and work out the interior angles.
Some of them you can get from what you are given, but I suspect the one you want will need the sine rule or the cosine rule.

If you get stuck - try doing a careful scale drawing with a ruler and protractor :)

I got all 3 of the angles. Are those the ones you are referring to?
 
  • #4
All three internal angles - inside the corners of the triangle?
<looks again> Oh I see ... so you are stuck on how to turn the angle into a bearing?

You have the plane angled 7.715 degrees north of the runway, and the runway is bearing 260 degrees ... so the plane is bearing ...? Don't worry about what the model answer says: what makes sense?
 
  • #5
I believe the official answer is wrong by 180 degrees. Looks like they did..

260 + 7.7 + 180 = 87.7

I believe the correct answer should be

260 + 7.7 = 267.7
 
  • #6
It would be good for OP's confidence to have that realisation instead of just being told though ;)
Part of the power of science is being able to overturn an authority.
 
  • #7
Simon Bridge said:
It would be good for OP's confidence to have that realisation instead of just being told though ;)
Part of the power of science is being able to overturn an authority.

Hahaha indeed, but thanks for the help everyone! I agree with why it is 267.7 but just in case I have posted the solution written by our professor:
XDjNI.png


In his diagram he shows that u vector points towards 267.7 however his answer ends up to be 87.7.
 
  • #8
The x-axis may well "point towards 80deg", but, in that case, the plane is traveling in the -x direction!

The -x axis is pointing at 260deg.
 
  • #9
Simon Bridge said:
The x-axis may well "point towards 80deg", but, in that case, the plane is traveling in the -x direction!

The -x axis is pointing at 260deg.

Ah okay, so he just mixed up the direction of u. Thanks a lot!
 
  • #10
I think it is the way the aviation do with direction.
Non-direction beacon (ndb) is used for aircraft to navigate TO the airport.
If you're heading to the airport, you heading according to NDB is heading to zero degree.

Here in the example, heading to runway 26(heading 260) equal to zero degree heading which means you are aligned with the runway.

Please correct me if I'm wrong.
 
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  • #11
Yeah - you could answer the question ... the aircraft is heading 7.7 degrees starboard of the runway direction on approach from the east end.

Sometimes you have a beacon, sometimes you use compass bearings to line you up.
This question defined a 0deg direction ... nothing to do with ndb, prof just mixed up the directions.

If the approach was from the west, the the heading would be 7.7 degrees port of the runway for a bearing of 82.3 degrees from north.
 
  • #12
azizlwl...

It asks "what heading should the pilot maintain"...

http://en.wikipedia.org/wiki/Aircraft_heading#Aircraft_heading

An aircraft's heading is the direction that the aircraft's nose is pointing.

It is referenced by using either the magnetic compass or heading indicator, two instruments that most aircraft have as standard. Using standard instrumentation, it is in reference to the local magnetic north direction. True heading is in relation to the lines of meridian (north-south lines). The units are degrees from north in a clockwise direction. East is 90, south is 180 and west is 270 degrees.

Sorry but the Prof is wrong. One possibility is he forgot that angles on a compass are measured clockwise where as in maths they are measured anticlockwise but that doesn't full explain it.
 
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  • #13
Yep - the trick now is challenging the prof.
There is a scientific way of challenging an authority ... but probably all that is needed is to ask the prof about which way the runway points and show him a diagram... phrase as a question.

The other concern is that there will be other questions like this: how do you protect against a mistake in the model answers?

One of the strategies is to write out, clearly, what your answer means instead of just leaving the finished number. Something the prof fails to model for his students.

He's not a bad teacher for all this - we all make mistakes and don't always cover the bases - and we all have different teaching styles. FWIW: the model answer is very clear in how the working is done ... I'd like to see more posts to PF like that. So I'd be interested to learn how he responds to being corrected: @theBeast: have you tried bringing this to his attention?
 

1. How do pilots know when it's time to start descending for a runway landing?

Pilots use a variety of instruments and techniques to determine when to descend for a runway landing. They typically rely on the instrument landing system (ILS) and their altimeters to determine their altitude and distance from the runway. They also use visual cues, such as the runway lights and approach lights, to guide their descent.

2. How long does it take for an airplane to land on a runway?

The time it takes for an airplane to land on a runway can vary depending on factors such as the type of aircraft, weather conditions, and air traffic control instructions. On average, it takes about 3-4 minutes from the time the airplane starts its descent to touchdown on the runway.

3. What happens if an airplane overshoots the runway during landing?

If an airplane overshoots the runway during landing, the pilot will likely perform a go-around, which involves increasing the airplane's altitude and circling back around to attempt the landing again. In rare cases, the airplane may need to divert to another airport for landing.

4. How do airplanes slow down after landing on a runway?

After touchdown, airplanes use a combination of techniques to slow down, including reverse thrust, braking, and spoilers. Reverse thrust is when the engines are temporarily set to push air forward, helping to slow the airplane down. Braking involves using the brakes on the wheels to slow the airplane down. Spoilers are panels on the wings that are raised to disrupt the airflow and help the airplane slow down.

5. Can airplanes land on runways in bad weather?

Airplanes are equipped with advanced technology and safety systems that allow them to land on runways in a variety of weather conditions. However, there are certain weather conditions, such as heavy fog or strong winds, that may make it unsafe for an airplane to land on a runway. In these cases, the pilot may need to divert to another airport or wait for the weather to improve before attempting the landing.

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