HP48-SX MES

[J. Veazey]

(The 48 is my office machine; I have an HP-50g at home for serious play).

I've got an application that seems to be tailor made for the Multi-Equation solver, yet MES consistently tells me I have too many unknowns.

This is a vector triangle problem, having to do with the placement of sonobuoys in front of an advancing convoy by an ASW helicopter, and the flight time and course of the helo.

Here are my 3 equations:

Ca=Sr+Vc*Slt+Vc*t

R=SQRT(Ca^2+D^2-2*Ca*D*cos(alpha))

t=R/Vh

My 3 unknowns are:

Ca - convoy advance

R - flight distance of helo to sonobuoy location

t - flight time of helo to sonobuoy location

All the rest of the variables above are known constants:

Sr - sonobuoy detection range

Vc - convoy speed

Slt - sonobuoy lifetime

D - Distance from convoy to helo at start

Vh - helo speed

alpha - Angle on the bow from the convoy to the helo

This system can be solved iteratively by just cycling thru the 3 equations to generate updated values of the unknowns. It usually takes about 7 or 8 iterations to converge to full displayed accuracy (which is way overkill).

I have set it all up in its own directory. I have done an MINIT, and an MITM just fine. When I punch MSOLV softkey, all the softkey labels act like they should, displaying all my variable names on white softkeys. I initialize the constants and those soft keys turn dark to show they are not variables.

When I try to solve via LS-ALL, I get the message "Too Many Unknowns". Trying to solve for a single variable also fails with the same message.

I have tried reordering the equations. No joy. I even added the other 2 angles in this vector triangle as unknowns, and more triangle relations (3 law of sines equations) and the equation Pi=sum(the angles in the triangle). I hoped this would help since I added just 2 more variables, and 4 equations. But, attempting to solver still gets the "Too Many Unknowns".

Am I doing something wrong, or is this system simply something that the MES can't handle? It seems too simple for that to be the problem, but ....

[Han]

Have you tried giving each of the unknowns an initial value (to be used as guesses)?

[J. Veazey]

I forgot to mention that step.

I initialized the unknowns with values I knew were very close to the answers; I also tried 0's, and other "reasonable" values.

I still got the "Too Many Unknowns" message when attempting to solve.

[Jean-Michel]

Hi,

probably isn't what follows the answer you're waiting from, but why don't you put the algebraic value of Ca and t into the equation of R ?
That would lead you to a simple second degree equation like :

K1.R^2 + K2.R + K3 = 0

where K1, K2 and K3 are constants which comes from the 3 equations you gave.

Regards.

[Mike Ingle]

I just posed a multiple-equation solver program that works on the 28 and 48. It might solve these equations.