Geoff, I have investigated your 4 sensor method, solved it, evaluated it for merit. A 4 sensor single plane open target would have many advantages. The sensors could be as small as the brackets and mount permanently on the target. I really tried to make it work, even if it wasn’t as accurate it would be a key step towards a $400 personal product.
Unfortunately it doesn’t work. There are symmetries involved that make it work everywhere except the center horizontal and vertical line on the target. Which is the place people aim at.
Not correct. It most certainly does work. In fact it works best in the centre of the target where the part of the isochronic curve (hyperbolas) we want to look at are in fact straight lines or close to it.
Who said anything about symmetries? Symmetry of what? Are you assuming that the positioning of the sensors are necessarily such that they form a regular square or rectangle? If so, you are wrong there also. The sensors - however many there may be - can be anywhere. We just need to know where they are relative to each other, and a reference point. Symmetry doesn't come into it. Nor do angles. Actually, it can help to not place the sensors in regular positions (such as at the corners of a regular rectangle) so as to not have any symmetry without in any way affecting the integrity of the result (if you're worried about it)
Multilateration is the mathematical basis of GPS, some anti-submarine warfare systems, and various other navigation systems. It is three-dimensional (trilateration is the two-dimensional version of it and either would work in an ET). It is used also by every other ET manufacturer other than (it seems ShotMarker and SMT). I wonder why? Are you seriously suggesting that everyone is wrong? (and that only you are right???) Your assertion that it "doesn't work" blows me away! It also has me question your credibility I'm afraid. I am not inclined to carry on with this discussion as a result, as I find it difficult to argue against this sort of thing (BS basically). After this post I think I will have to withdraw (to the cheers I am sure of some people reading all this).
Smarter mathematical minds than yours or mine have established these mathematical and engineering principles and methods. Sir Issac Newton comes to mind - in fact he developed the very method that I use a few hundred years ago. These are not new concepts.
I think you are attempting to divert focus away from your non-isochronic method that is dependent (it seems) on a potentially erroneous input parameter and simply bringing up phurphies to discredit something it seems you really don't know too much about. You are also discounting the very desirable byproducts that that multilateration can provide.
I suspect you don't know how to do it. If you did you would - there is no extra cost involved. Having Vt is certainly a nice number to have but it should not be essential in the event that it just might be wrong! (without you knowing).
Requiring a precise input value such a measured terminal velocity in order to make your mathes work is an unnecessary risk to the integrity of he result - just in case the velocity measurement is wrong. How do you know it is right and thus provide confidence that your resulting impact point is correct? Another input that has to be measured and used is air temperature and both methods require it.
Since (from an engineering perspective) error always accumulate it makes sense to remove where possible any sources of error. Errors never detract from each other. Vt is an obviously source of error and is easily removed from the equation - if the right equation (or method) is used that doesn't require it in the first place. How do you know that your Vt value is correct? I know of at least one of your systems here in Australia that has reported a terminal velocity higher than the muzzle velocity (that was measured by both a labradar and chronograph) and in that instance your software didn't pick it up.
You will always have errors in any system. We strive to minimise them, or at least their sources. Again, why would you risk the integrity of your result by utilising a potential major source of error when you don't have to?
Is this the sort of vulnerability you want in a system that is being seriously considered for use with the settings of state or national records?
I am sorry for those of you that don't want to hear any of this. But the fact is for this application multilateration is the best (or at least a better) engineering approach to the problem. Don't take just my word for it - perhaps ask any engineer or mathematician who knows what it is and how/where it can be applied.
I can't believe I have engaged in this argument - I have people advising me (in fact telling me) to stop it (and not because they are afraid of what I say and/or don't want to hear it). Yes it is a valid argument, but I think for me the bones of the horse have now been picked clean and we are not going to get to 30 pages. At least not on my account.