Analog Computation of Missile Launch Angle - Page 1
Forum section: electronics / projects

author: TimNJ
author_rank: Super Contributor
timestamp: March 17, 2016, 08:16:55 pm
content: Hi guys,I've been working on the sequel to my circuit analysis video I made about a year ago. This one is basically on op-amps with a brief bit about transistor amplifiers and dependent sources.One thing I want to talk about is the past applications of op-amps, most notably, in analog computation. One application was in launching ballistic missiles, where an analog computer would calculate the correct angle relative to the surface of the earth.So I was looking through a book I have on analog computation and I found the example 5-3, that asks just that. So I tried deriving a computational block diagram that would solve this problem, but I'm a bit stuck, and I was wondering if anyone could point me in the right direction.I know we want to find theta at the time t when y(t) = 0. Just not sure how to interpret that in a block diagram. Also, does anyone hae any idea of how to realize cos(theta) in hardware?Thanks,Tim

author: dmills
author_rank: Super Contributor
timestamp: March 17, 2016, 09:40:29 pm
content: Missiles or cannon shells (It makes a huge difference because a shell does not have a meaningful boost phase with a complex acceleration profile).For a shell (Ignoring air resistance and several other unfortunate effects) the horizontal component of the velocity is constant Vm * cos theta.Given this the time of flight, T = range / (Vm * cos Theta)Now consider the vertical component, at launch it is Vm * sin theta, upwards and the acceleration is 1g downward, but note that the parabola is symmetrical in this case as launch and target are at the same elevation, so the vertical speed will drop to 0 at the highest point, clearly given by Thp = (Vm * sin theta) / g and the time of impact T is then 2 * Thp = 2*Vm * sin Theta / g.Equating the two expressions for T:range / (Vm cos Theta) = 2* (Vm * sin Theta) / gMultiply by Vm * cos Thetarange = 2 * Vm^2 * sin Theta * cos Theta / gBut 2 * sin Theta * cos Theta = sin (2 * Theta),so range = Vm^2 * sin (2 * Theta) / gTheta = arcsin (range * g / Vm^2) / 2Somebody check my working please.Regards, Dan.

author: TimNJ
author_rank: Super Contributor
timestamp: March 17, 2016, 10:44:37 pm
content: Thanks Dan!Went through all your work, including having some "duh" moments, as I had some flashbacks to introductory physics. It looks good to me. Thanks for your efforts.The Vm^2 might be a little troubling for the sake of this video since that requires multiplication and not just amplification (by some constant).Probably more concerning is performing an arcsin operation in analog. I guess this book assumes that a hardware block can be created for almost any mathematical function.Thanks again.

author: German_EE
author_rank: Super Contributor
timestamp: March 17, 2016, 10:48:20 pm
content: Strange how history repeats itself. ENIAC was digital rather than analog but its first use was computing firing tables for the US Army.

author: dmills
author_rank: Super Contributor
timestamp: March 17, 2016, 11:15:47 pm
content: Make the Vm input a double gang pot with the wiper of the first gang buffered and then fed to the top of the second gang, wiper of the second gang is then square law in terms of the voltage on the top of the first gang and the rotation of the pot?The arcsin function looks like a job for some sort of piecewise approximation to me, a good opportunity to mess with a pile of diodes and resistors.For a truly amazing mechanical system that did all this stuff, for real, and even compensated wear on the gun tubes, the ford Rangekeeperhttps://en.wikipedia.org/wiki/Rangekeeperis interesting.73 Dan.

author: RobK_NL
author_rank: Frequent Contributor
timestamp: March 18, 2016, 10:28:57 am
content: I once had the good fortune of getting a guide tour of the control system of theGoalkeeper system. It used a massive amount of servo-type potmeters with trigonometric tapers. Those thing cost an absolute fortune back then.Probably still dohttp://www.altheris.com/c/Sensors-Rotation-sensors/SIN-COS-potentiometers/40547/

author: dmills
author_rank: Super Contributor
timestamp: March 18, 2016, 03:03:26 pm
content: We have an old audio product that uses a sine/cos pot, and yea, they are not exactly the cheapest thing imaginable.Regards, Dan.

author: wolf32d
author_rank: Contributor
timestamp: March 18, 2016, 05:09:01 pm
content: Quote from: dmills on March 17, 2016, 09:40:29 pmYour calculations are fine!In addition: the max range is given byrange_max = Vm^2 * sin (2 * Theta) / g = 31080 ft = 0,4905 milesi.e. vhen Vm = 1000 ft/s and Theta = 45°

author: GK
author_rank: Super Contributor
timestamp: March 19, 2016, 11:51:39 pm
content: Nice to see you've hunted down a copy of G. R. PetersonsBasic Analog Computation.

author: ChunkyPastaSauce
author_rank: Unknown
timestamp: March 20, 2016, 12:09:31 am
content: WW2 ships firing ballistics greater than 5 in diameter, part of the calculation by the analog computer included correction for earth rotation if there was a north-south component.... not that you have to do that but I thought it was kinda interesting.http://archive.hnsa.org/doc/firecontrol/partc.htmhttp://archive.hnsa.org/doc/firecontrol/

author: Raj
author_rank: Frequent Contributor
timestamp: May 13, 2016, 07:39:39 am
content: I don't know much about it but i do know that the military uses a set of special rulers (4 rulers) that they keep on the map and slide it to determine the angle of cannonwhy 4 rulers?a single ruler represents a certain quantity of propellent charge,propellent charges comes in packages of set amount,maximum number of charge a gun can accommodate is 4 packsfor rockets, its gonna be harder. try using java for such stuffmake an android app with it's screen being a ruler

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 13, 2016, 08:16:32 am
content: Analog computation is fun, because you can consider many types of circuits to solve a particular function or expression.There are ways to implement cos(x), yes. One continuous method is based on a chain of differential BJTs, arranged so that their delta Ic = tanh(Vin) curves obey an identity, which converts them into an approximated region of cos(x) or sin(x), as the case may be. The approximation resembles a Taylor series approximation, with about N zeroes/crossings/"cycles" for N stages wired together, and quite good accuracy/convergence for inputs near zero.One obvious time-discontinuous method, is to simply sample-and-hold a sine wave.If you get stuck thinking everything has to be continuous and implicit, you'll miss out on easy tricks like this! Caveats are: you need a very low distortion sine wave source; you need a precision synchronized timer, triggered by the sine wave's zero crossing (or a peak, as the case may be), and producing a delay proportional to the input signal; you need a S&H with precise enough action (small aperture window, low charge injection); and you need a follower and filter suitable for the sample rate and/or settling time desired.You can also use delayed sampling to generate interesting exponents (like, sampling an RC charge/discharge curve), without having to use matched diode or transistor pairs.Of course, any time you have a regular function, you can find its inverse by placing it in an op-amp feedback loop. The bandwidth (or settling time) goes down accordingly (and may be rather troublesome to deal with, as the loop gain varies with condition -- potentially making it unstable in one case, or making the settling time prohibitively slow in the other!), but this is a good way, for example, to generate a division or square root function, starting with a multiplier block.Tim

author: Raj
author_rank: Frequent Contributor
timestamp: May 14, 2016, 03:13:26 am
content: I was thinking, if it's a missile, it should go straight until it's fuel goes out... try making an analogue gyroscopic stabilizer that makes it go straight