| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
First posted in Brain_bogglers.. STILL UNSOLVED!
H E L P !!
DJBROWN
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Note 893.0 Rocket altitude measurements via ground telemetry 6 replies
SNELL::DJBROWN 55 lines 23-FEB-1990 14:01
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Here's a little 3D geometry problem that's been puzzling me for
a while.
I like to dabble a little in model rocketry. As such, I wish
to devise a method for determining the altitude my rockets get
to. All I have at my disposal is a little Angle_meter that I use
to track the rocket in flight, and then to pull the trigger (when
the chute deploys) to lock in this angle (measured off of the
horizontal) so that the angle at deployment can be read.
SEE CRUDE DIAGRAM NEXT PAGE..
^
||
/||\
/ .
. ^
/ . |
Tracking . |
Gun . H
| / . |
| . v
v \
/ \ <--Angle THETA
// | . Height = D * Tan(THETA)
O / |
+/ <--D-->
| |
/\ <-ME | Launch site
========================================================
This method is erroneous because the rockets usually fly maybe
hundreds of yards downfield horizontally, thus nullifying this simple
trigonometric method.
My postulation... If I were to have THREE such 'Angle-meters', at
three different but known locations on the launch field, can the rocket
height be calculated by trig methods by knowing the 'angles off
horizontal' from each of the three meters, and by knowing the (x,y,0)
locations of each tracker? If so, what is that equation? and
where should the trackers be located? (I like to consider the launch
location as coordinate (0,0,0).
I hope this seems clear. I really seem hung up on the math. Any
insight would be appreciated.
Actually, Im hoping to have a rocket contest within my son's
cubscout troup in a couple months. So, please... HELP!
Dave J Brown
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| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1207.1 | HPSTEK::XIA | In my beginning is my end. | Wed Mar 07 1990 18:05 | 5 | |
re .0,
Yes, you can do it with three. However, if you can also obtain the
horizontal angle, you only need two, and the calculation is much
simpler with this method.
Eugene
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| 1207.2 | HPSTEK::XIA | In my beginning is my end. | Wed Mar 07 1990 18:20 | 3 | |
I think your real problem will be the synchronization of your
measurements.
Eugene
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| 1207.3 | ALIEN::POSTPISCHIL | Always mount a scratch monkey. | Wed Mar 07 1990 21:42 | 10 | |
I discussed this with Brian McCarthy, who also pursues rocketry as a
hobby, and he said that somebody did a study on the use of two
measurements compared to three. Theoretically, three measurements can
produce an exact answer whereas two can give an answer only if certain
assumptions are made. However, the study found that two measurements
does in fact give a good result -- apparently the calculations for
three measurements are not stable.
-- edp
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| 1207.4 | CHOVAX::YOUNG | An Urban Legend in my own time. | Wed Mar 07 1990 23:15 | 5 | |
Re .3:
Is that with or without the horizontal measurement of .1 ?
-- Barry
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| 1207.5 | BEING::POSTPISCHIL | Always mount a scratch monkey. | Thu Mar 08 1990 07:51 | 6 | |
Re .4:
I think it is without, but I'm not sure.
-- edp
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| 1207.6 | 4GL::GILBERT | Ownership Obligates | Thu Mar 08 1990 08:33 | 7 | |
Re .4, .5:
For two measurements of declination (?) without the horizontal angle
(azimuth), you essentially know two cones. They don't intersect in
a single point -- you need the azimuths or a third declination.
Anyway, I expect the original poser still wants some equations.
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| 1207.7 | ex | FIVER::DJBROWN | Thu Mar 08 1990 14:40 | 9 | |
Yup, an equation is really what I need. (One I can put into my
TI58C for use on the field). I have at my disposal ONLY the Single
angle tracker (3x) that is built my the model rocket mfr.
Synchronization I wouldnt anticipate to be a problem because all
three trackers pull their triggers at the very instant they see
the retro-charge POP the chute out (Lots of smoke, very evident!)
DJ Brown
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| 1207.8 | BEING::POSTPISCHIL | Always mount a scratch monkey. | Fri Mar 09 1990 08:15 | 13 | |
Re .6:
I believe some assumption is made about the position of the rocket.
For example, you do not need to completely determine the rocket's
position, just its altitude. If at least one measurement is
sufficiently far away from the launch site, the intersection of the
cone from that measurement with the other cone may be close enough to
horizontal that all points in the intersection are within a desired
degree of accuracy. (Should the other cone be very near the launch
site?)
-- edp
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| 1207.9 | Brute Force Sucks | FIVER::DJBROWN | Mon Mar 12 1990 12:50 | 9 | |
OK, So Ive reduced it to the following three simultaneous equations..
A1x� + B1x + C1y� + D1y + E1z� + F1z = K1 equation 1
A2x� + B2x + C2y� + D2y + E2z� + F2z = K2 equation 2
A3x� + B3x + C3y� + D3y + E3z� + F3z = K3 equation 3
Can this be solved for (x,y,z) ??
Dave "IMAROKITMAN" Brown
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| 1207.10 | HPSTEK::XIA | In my beginning is my end. | Mon Mar 12 1990 13:46 | 5 | |
re -1,
As you may have already found out, few people are interested in solving
things with brute force. Around here we tend to describe the method
and leave others to fill in the details. :-)
Eugene
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| 1207.11 | SIMPLE GEOMETRY | FDCV01::ADUBE | Wed Mar 14 1990 13:40 | 23 | |
. If you have two observers(O1 & O2) on the same
.. horizontal plane as the rocket launch and a distance
. .. of "a" you can determine "h" by measuring the
. . horizontal angles "A" and "B" when you measure
. . . the verticle angles "D" and "E". (note: you won't
. h. need angle "E" just "A" "B" and "D").
. . .
. . .
. . . .E. The equation is h=( a * TAN(B) ) TAN(D)
. D. . . -------------- * ------
. . . .. (TAN(B)+TAN(A)) COS(A)
.. A . B .
...................
O1 a O2
All angles are taken at rocket lauch level, therefore if you have two obsevers
each looking at the rocket measuring the angles(A,B, and D) 5 feet off the
ground, true h=h+5ft.
Locate the observers upwind from the launch pad so that angle A and B are not 0.
AL
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