| Topic: |
Science > Physics |
| User: |
"RMW" |
| Date: |
12 Apr 2007 01:09:54 PM |
| Object: |
Elevation question regarding airplane |
Good day!
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
I'm just assuming that this is an ideal scenario where the plane is
above some great plains (flat land) that is more than 70 miles wide
from each direction. I'm also assuming that the plane does not roll
and is just hovering above the ground at the same location. The only
thing that changes with the plane is its height.
Also, I'm defining elevation angle as the angle formed by drawing a
straight line from the airplane and the ground directly beneath it and
another line from the plane towards the ground location where the beam
is pointing.
I also would like to know how I can calculate this, too.
Thanks!
.
|
|
| User: "Nomal Sapeton" |
|
| Title: Re: Elevation question regarding airplane |
12 Apr 2007 01:27:44 PM |
|
|
"RMW" <mr.whatever@gmail.com> wrote in message
news:1176401394.639162.229040@w1g2000hsg.googlegroups.com...
Good day!
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
of course, especially when it is 5 miles up.
I'm just assuming that this is an ideal scenario where the plane is
above some great plains (flat land) that is more than 70 miles wide
from each direction. I'm also assuming that the plane does not roll
and is just hovering above the ground at the same location. The only
thing that changes with the plane is its height.
you said elevation angle, not elevation
Also, I'm defining elevation angle as the angle formed by drawing a
straight line from the airplane and the ground directly beneath it and
another line from the plane towards the ground location where the beam
is pointing.
I also would like to know how I can calculate this, too.
Thanks!
It is highshool trig look up sin or cos
.
|
|
|
|
| User: "Androcles" |
|
| Title: Re: Elevation question regarding airplane |
12 Apr 2007 03:09:42 PM |
|
|
"RMW" <mr.whatever@gmail.com> wrote in message =
news:1176401394.639162.229040@w1g2000hsg.googlegroups.com...
Good day!
=20
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
Of course. So will any movement of the plane. After all,=20
the same plane flying over London will not illuminate Sydney until
it gets to Sydney.
Any reason for it to be a laser and not a searchlight?
=20
I'm just assuming that this is an ideal scenario where the plane is
above some great plains (flat land) that is more than 70 miles wide
from each direction. I'm also assuming that the plane does not roll
and is just hovering above the ground at the same location. The only
thing that changes with the plane is its height.
=20
Also, I'm defining elevation angle as the angle formed by drawing a
straight line from the airplane and the ground directly beneath it and
another line from the plane towards the ground location where the beam
is pointing.
=20
I also would like to know how I can calculate this, too.
tan(theta) =3D height/base, theta being the angle from the beam to=20
the horizon.
.
|
|
|
| User: "RMW" |
|
| Title: Re: Elevation question regarding airplane |
17 Apr 2007 11:52:05 AM |
|
|
On Apr 12, 4:09 pm, "Androcles" <Engin...@hogwarts.physics.co.uk>
wrote:
Of course. So will any movement of the plane. After all,
the same plane flying over London will not illuminate Sydney until
it gets to Sydney.
Any reason for it to be a laser and not a searchlight?
It was just a conceptual idea for a 3D flying game that my friends and
I were discussing.
tan(theta) = height/base, theta being the angle from the beam to
the horizon.
Thanks!
.
|
|
|
| User: "Androcles" |
|
| Title: Re: Elevation question regarding airplane |
17 Apr 2007 12:12:07 PM |
|
|
"RMW" <mr.whatever@gmail.com> wrote in message =
news:1176828724.964057.176280@p77g2000hsh.googlegroups.com...
On Apr 12, 4:09 pm, "Androcles" <Engin...@hogwarts.physics.co.uk>
wrote:
Of course. So will any movement of the plane. After all,
the same plane flying over London will not illuminate Sydney until
it gets to Sydney.
Any reason for it to be a laser and not a searchlight?
=20
It was just a conceptual idea for a 3D flying game that my friends and
I were discussing.
=20
=20
tan(theta) =3D height/base, theta being the angle from the beam to
the horizon.
=20
Thanks!
Get Google SketchUp,=20
http://sketchup.google.com/
Draw a plane and beam, create a group and then rotate it.
I'm doing all my animations in SketchUp these days, you can see some =
here:
http://www.androcles01.pwp.blueyonder.co.uk/
.
|
|
|
|
|
|
| User: "Ben Newsam" |
|
| Title: Re: Elevation question regarding airplane |
12 Apr 2007 05:35:04 PM |
|
|
On 12 Apr 2007 11:09:54 -0700, "RMW" <mr.whatever@gmail.com> wrote:
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
This is homework, isn't it?
.
|
|
|
| User: "RMW" |
|
| Title: Re: Elevation question regarding airplane |
17 Apr 2007 11:49:32 AM |
|
|
On Apr 12, 6:35 pm, Ben Newsam <ben.new...@ukonline.co.uk> wrote:
On 12 Apr 2007 11:09:54 -0700, "RMW" <mr.whate...@gmail.com> wrote:
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
This is homework, isn't it?
No, not homework. But really, what I'm curious about is that if we
were to create a 3D game and the space ship continuously is shooting a
laser down the ground, how much will the laser be redirected if the
plane changes orientation?
Thanks!
.
|
|
|
| User: "CWatters" |
|
| Title: Re: Elevation question regarding airplane |
18 Apr 2007 03:46:33 PM |
|
|
"RMW" <mr.whatever@gmail.com> wrote in message
news:1176828572.435876.45520@y80g2000hsf.googlegroups.com...
On Apr 12, 6:35 pm, Ben Newsam <ben.new...@ukonline.co.uk> wrote:
On 12 Apr 2007 11:09:54 -0700, "RMW" <mr.whate...@gmail.com> wrote:
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
This is homework, isn't it?
No, not homework. But really, what I'm curious about is that if we
were to create a 3D game and the space ship continuously is shooting a
laser down the ground, how much will the laser be redirected if the
plane changes orientation?
Try watching the Dam Busters movie.
.
|
|
|
| User: "John C. Polasek" |
|
| Title: Re: Elevation question regarding airplane |
19 Apr 2007 01:21:19 PM |
|
|
On Wed, 18 Apr 2007 21:46:33 +0100, "CWatters"
<colin.watters@turnersNOSPAMoak.plus.com> wrote:
"RMW" <mr.whatever@gmail.com> wrote in message
news:1176828572.435876.45520@y80g2000hsf.googlegroups.com...
On Apr 12, 6:35 pm, Ben Newsam <ben.new...@ukonline.co.uk> wrote:
On 12 Apr 2007 11:09:54 -0700, "RMW" <mr.whate...@gmail.com> wrote:
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
This is homework, isn't it?
No, not homework. But really, what I'm curious about is that if we
were to create a 3D game and the space ship continuously is shooting a
laser down the ground, how much will the laser be redirected if the
plane changes orientation?
Try watching the Dam Busters movie.
1 degree is about 1/60th radian, so at 5000 ft it would move
(5000/60)*1.414 (for secant of 45 degrees) = m/l 700/6 =116 ft,
.
|
|
|
|
|
| User: "Ben Newsam" |
|
| Title: Re: Elevation question regarding airplane |
17 Apr 2007 02:02:18 PM |
|
|
On 17 Apr 2007 09:49:32 -0700, RMW <mr.whatever@gmail.com> wrote:
On Apr 12, 6:35 pm, Ben Newsam <ben.new...@ukonline.co.uk> wrote:
On 12 Apr 2007 11:09:54 -0700, "RMW" <mr.whate...@gmail.com> wrote:
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
This is homework, isn't it?
No, not homework. But really, what I'm curious about is that if we
were to create a 3D game and the space ship continuously is shooting a
laser down the ground, how much will the laser be redirected if the
plane changes orientation?
OK, let's assume the plane is 100 metres or other unit above the
ground, and the laser is, as you say, at an angle of 45 degrees. You
should be able to convince yourself that the laser hits the ground 100
units away from the place on the ground above which the plane is.
If you draw it as a diagram from the side, you should be able to show
a right-angled triangle of the plane (in the air), the point on the
ground directly below the plane, and the point where the laser hits.
With a right-angled triangle, tan theta = opposite side over adjacent
side, the angle theta would be the angle between the laser shot and
the ground, in this case 45 degrees. 100/ tan 45 = 100
If the plane shoots one degree higher, the angle between the laser and
the ground will be one degree less. 100/ tan 44 = ???
The location changes by the difference, obviously.
Although presumably the plane's altitude isn't always 100, you can
work it out the same way whatever the actual numbers are.
.
|
|
|
|
| User: "Randy Poe" |
|
| Title: Re: Elevation question regarding airplane |
17 Apr 2007 02:39:25 PM |
|
|
On Apr 17, 12:49 pm, RMW <mr.whate...@gmail.com> wrote:
On Apr 12, 6:35 pm, Ben Newsam <ben.new...@ukonline.co.uk> wrote:
On 12 Apr 2007 11:09:54 -0700, "RMW" <mr.whate...@gmail.com> wrote:
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
This is homework, isn't it?
No, not homework. But really, what I'm curious about is that if we
were to create a 3D game and the space ship continuously is shooting a
laser down the ground, how much will the laser be redirected if the
plane changes orientation?
If it's hitting the ground at a shallow angle, the answer is
"quite a lot". Using the tangent function properly as others have
suggested should tell you that.
For instance, suppose the beam is pointed at 45 degrees below
horizontal and the space ship is 1000 meter above ground. The
horizontal distance, the point where the beam strikes, is at
1000/tan(45 deg) = 1000 m.
Suppose the space ship now tilts by 0.1 degree, and the grazing
angle goes to 44.9 deg. Then the horizontal distance is now
1000/tan(44.9 deg) = 1003.5 m. (Shallower angle means the
beam hits the ground farther away). Not a huge movement.
But now suppose the beam was at a shallow angle to begin
with, say 5 deg. The impact point is at 1000/tan(5 deg)
= 11430 m. If the space ship tilts by 0.1 deg, the impact point
moves to 1000/tan(4.9 deg) = 11664 m, a distance of 234 m
from a change of only a tenth of a degree!
- Randy
.
|
|
|
|
|
|
| User: "Randy Poe" |
|
| Title: Re: Elevation question regarding airplane |
12 Apr 2007 03:17:07 PM |
|
|
On Apr 12, 2:09 pm, "RMW" <mr.whate...@gmail.com> wrote:
Good day!
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
I'm just assuming that this is an ideal scenario where the plane is
above some great plains (flat land) that is more than 70 miles wide
from each direction. I'm also assuming that the plane does not roll
and is just hovering above the ground at the same location. The only
thing that changes with the plane is its height.
Also, I'm defining elevation angle as the angle formed by drawing a
straight line from the airplane and the ground directly beneath it and
another line from the plane towards the ground location where the beam
is pointing.
I also would like to know how I can calculate this, too.
This +-1 degree sweeps out an arc. The length of that arc
at distance d is d*theta, where theta is the angular width of
the arc in radians.
1 degree = 0.01745 radians, so if the beam is pointing to
a spot 10 miles away, a 1 degree shift will move the spot
10*0.01745 = 0.1745 miles on the ground (921 feet).
- Randy
.
|
|
|
| User: "Greg Neill" |
|
| Title: Re: Elevation question regarding airplane |
12 Apr 2007 03:57:19 PM |
|
|
"Randy Poe" <poespam-trap@yahoo.com> wrote in message
news:1176409027.812610.325560@d57g2000hsg.googlegroups.com...
On Apr 12, 2:09 pm, "RMW" <mr.whate...@gmail.com> wrote:
Good day!
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
I'm just assuming that this is an ideal scenario where the plane is
above some great plains (flat land) that is more than 70 miles wide
from each direction. I'm also assuming that the plane does not roll
and is just hovering above the ground at the same location. The only
thing that changes with the plane is its height.
Also, I'm defining elevation angle as the angle formed by drawing a
straight line from the airplane and the ground directly beneath it and
another line from the plane towards the ground location where the beam
is pointing.
I also would like to know how I can calculate this, too.
This +-1 degree sweeps out an arc. The length of that arc
at distance d is d*theta, where theta is the angular width of
the arc in radians.
1 degree = 0.01745 radians, so if the beam is pointing to
a spot 10 miles away, a 1 degree shift will move the spot
10*0.01745 = 0.1745 miles on the ground (921 feet).
The ground is not on the locus of the arc at a fixed
radius d...
.
|
|
|
|
| User: "Androcles" |
|
| Title: Re: Elevation question regarding airplane |
12 Apr 2007 03:53:23 PM |
|
|
"Randy Poe" <poespam-trap@yahoo.com> wrote in message =
news:1176409027.812610.325560@d57g2000hsg.googlegroups.com...
On Apr 12, 2:09 pm, "RMW" <mr.whate...@gmail.com> wrote:
Good day!
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
I'm just assuming that this is an ideal scenario where the plane is
above some great plains (flat land) that is more than 70 miles wide
from each direction. I'm also assuming that the plane does not roll
and is just hovering above the ground at the same location. The only
thing that changes with the plane is its height.
Also, I'm defining elevation angle as the angle formed by drawing a
straight line from the airplane and the ground directly beneath it =
and
another line from the plane towards the ground location where the =
beam
is pointing.
I also would like to know how I can calculate this, too.
=20
This +-1 degree sweeps out an arc. The length of that arc
at distance d is d*theta, where theta is the angular width of
the arc in radians.
=20
1 degree =3D 0.01745 radians, so if the beam is pointing to
a spot 10 miles away, a 1 degree shift will move the spot
10*0.01745 =3D 0.1745 miles on the ground (921 feet).
=20
- Randy
Planes these don't often fly at 10 miles high, but those that do are=20
called "U2".
30,000 ft or 5-6 miles is a more reasonable round figure.
Mount Everest - Elevation: 8,850 M (29,035 feet)=20
tan 46 * 30,000 =3D 31065.909
tan 44 * 30,000 =3D 28970.663
2095.246 feet.
tan 46 * 52,800 =3D 54676.000
tan 44 * 52,800 =3D 50988.367
3687.6 feet.=20
3687/921 * 50 =3D 200% error, Poe.
Can I help you with your finances?
.
|
|
|
|
|
| User: "Sam Wormley" |
|
| Title: Re: Elevation question regarding airplane |
12 Apr 2007 02:09:11 PM |
|
|
RMW wrote:
Good day!
If a laser beam is mounted on an airplane and is installed in a 45
degree angle pointed towards the ground, will a slight change in
elevation angle (about +/- 1 degree) significantly alter the location
of the beam on the ground?
I'm just assuming that this is an ideal scenario where the plane is
above some great plains (flat land) that is more than 70 miles wide
from each direction. I'm also assuming that the plane does not roll
and is just hovering above the ground at the same location. The only
thing that changes with the plane is its height.
Also, I'm defining elevation angle as the angle formed by drawing a
straight line from the airplane and the ground directly beneath it and
another line from the plane towards the ground location where the beam
is pointing.
I also would like to know how I can calculate this, too.
Thanks!
Draw a diagram... use trig.
.
|
|
|
|
|
Related Articles |
|
|
