Zero gyro shooting

[Dorjun Driver]

This is the quick and not–so–dirty method I use. I've found it quite handy when the tactical situation gets chaotic.

Plug the formula into your fx-5000F or smart phone and Bob’s your uncle. Heck, grab a pack of Lucky’s, a cup a joe, whip out the old slip-stick and do it old school!



Don't let the trigonometry intimidate you. After a couple of patrols you may find yourself solving this in your head.

I hope you find it useful.

[Carrollsue]

Yep, that's it

[fireftr18]

Thanks for all the work.

[TorpX]

I see someone else has been putting their high school geometry to good use.

I like your diagram there. I assume the " fx-5000F " is your calculator. I have used my TI-85 very successfully since my SHCE days, but now, every time I want to add something to it, I have to find something to delete.

[Dorjun Driver]

Originally Posted by TorpX

I see someone else has been putting their high school geometry to good use.

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.
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There are some interesting hacks one may use to eliminate the above trig functions altogether. But seeing as this formula is only executed a couple of times per hour, the effort to include them far outweighed their utility.

[Dignan]

Hey Dorjun. Do you know if the "asin" function is the same as "arcsin"? I'm trying to replicate your formula in a smartphone calculator and it only has an asin function. I'm not getting the correct solution in my tests and I'm wondering if this is why. Math was never my strength.

EDIT: another question... I am building my formula using letters for my variables. V for ship velocity, T for Torp speed. This seems to work fine but for track angle do I need to attach some trig function so the calculator knows its an angle and not a quantity? I've just been using "A" for track angle but I don't know if the formula is understanding this as an angle. Is this my problem by chance?

[Pisces]

Asin, arcsin, sin with superscript -1 aka inv(erse) sine, all means the same function. It calculates an angle that corresponds with the slope of a vertical edge divided by the length of the sloping side (hypotenusa) in a right angled triangle. Though it can also be used with triangles that have no right angle (90 degrees) in them. The 'slope' must have a a value between -1 and 1, or else the angle cannot be calculated. No butts, no ifs, it can't!

In everyday household uses, the sine/cosine/tangent functions are calculated on degrees. As such the reverse kind of function: asin/acos/atan result in degrees. But most scientific calculators also have an option make them use angles in radians. A radian is the angle made when you wrap the radius of a circle around the circumference. Radians are a big thing in engineering and science. It's 57.29577951 degrees, or 180 degrees divided by Pi. 2 Pi radians make a full circle. On Casio calculators there should be a small 3 character abreviation in the top of the display: deg for degrees, rad for radians and gra for gradians. Gradians are a big thing in surveying.

To test your calculator for degree or radian mode: 0.707 asin should result in near 45 degrees, or 0.785398163 radians (=Pi/4), or 50 gradians (90 degrees angle is 100 gradians. The French trying to be funny there.)

So that could be the cause for unexpected results from the formula. Or the order of precedence in arithmetic: multiplication/division precedes adding/subtracting.

[Carrollsue]

Originally Posted by Pisces

Asin, arcsin, sin with superscript -1 aka inv(erse) sine, all means the same function. It calculates an angle that corresponds with the slope of a vertical edge divided by the length of the sloping side (hypotenusa) in a right angled triangle. Though it can also be used with triangles that have no right angle (90 degrees) in them. The 'slope' must have a a value between -1 and 1, or else the angle cannot be calculated. No butts, no ifs, it can't!

In everyday household uses, the sine/cosine/tangent functions are calculated on degrees. As such the reverse kind of function: asin/acos/atan result in degrees. But most scientific calculators also have an option make them use angles in radians. A radian is the angle made when you wrap the radius of a circle around the circumference. Radians are a big thing in engineering and science. It's 57.29577951 degrees, or 180 degrees divided by Pi. 2 Pi radians make a full circle. On Casio calculators there should be a small 3 character abreviation in the top of the display: deg for degrees, rad for radians and gra for gradians. Gradians are a big thing in surveying.

To test your calculator for degree or radian mode: 0.707 asin should result in near 45 degrees, or 0.785398163 radians (=Pi/4), or 50 gradians (90 degrees angle is 100 gradians. The French trying to be funny there.)

So that could be the cause for unexpected results from the formula. Or the order of precedence in arithmetic: multiplication/division precedes adding/subtracting.

OMG….you took me back 45years to Trig class, with me with the huh look on my face!!
Thanks

[Dignan]

Originally Posted by Pisces

Asin, arcsin, sin with superscript -1 aka inv(erse) sine, all means the same function. It calculates an angle that corresponds with the slope of a vertical edge divided by the length of the sloping side (hypotenusa) in a right angled triangle. Though it can also be used with triangles that have no right angle (90 degrees) in them. The 'slope' must have a a value between -1 and 1, or else the angle cannot be calculated. No butts, no ifs, it can't!

In everyday household uses, the sine/cosine/tangent functions are calculated on degrees. As such the reverse kind of function: asin/acos/atan result in degrees. But most scientific calculators also have an option make them use angles in radians. A radian is the angle made when you wrap the radius of a circle around the circumference. Radians are a big thing in engineering and science. It's 57.29577951 degrees, or 180 degrees divided by Pi. 2 Pi radians make a full circle. On Casio calculators there should be a small 3 character abreviation in the top of the display: deg for degrees, rad for radians and gra for gradians. Gradians are a big thing in surveying.

To test your calculator for degree or radian mode: 0.707 asin should result in near 45 degrees, or 0.785398163 radians (=Pi/4), or 50 gradians (90 degrees angle is 100 gradians. The French trying to be funny there.)

So that could be the cause for unexpected results from the formula. Or the order of precedence in arithmetic: multiplication/division precedes adding/subtracting.

<-- is my face right now. I think I am beginning to understand what you are saying. I'm going to re-read this later and try to digest. Thanks for the explanation. So what I've done is plug this formula by Dorjun into an app called MagiCALc. It's a scientific calculator for the iphone. Here's what I've got.

Lead Angle = asin (V sin A / (V ^ 2 + T ^ 2 - 2VT cos A) ^ 1/2)
V= Target speed
T= Torpedo Speed
A= Track angle/Intercept angle.

The program automatically recognizes my variables and asks for input. When I input the following values for each as a test...

V(Target speed) = 9
T (Torp speed) = 30
A (Intercept angle) = 75

...it spits out (= -0.11)
I take this to mean an 11 degree lead angle. Is that how I should be doing this?

I tried it with a different lead angle variable again to be sure.
V(Target speed) = 9
T (Torp speed) = 30
A (Intercept angle) = 135

and it spit out (=0.02). or a 2 degree lead angle
That doesn't seem right to me. Can anyone see what I've done wrong here? Is my formula off? Do I need to make the calculator see my output "Lead Angle" as an angle and not a straight number value or something?

Pisces, thanks again for the trig refresher. While I love playing this game, this has reminded me why I was a "social science" person.

[Dorjun Driver]

Originally Posted by Dignan

<-- is my face right now. I think I am beginning to understand what you are saying. I'm going to re-read this later and try to digest. Thanks for the explanation. So what I've done is plug this formula by Dorjun into an app called MagiCALc. It's a scientific calculator for the iphone. Here's what I've got.

Lead Angle = asin (V sin A / (V ^ 2 + T ^ 2 - 2VT cos A) ^ 1/2)
V= Target speed
T= Torpedo Speed
A= Track angle/Intercept angle.

The program automatically recognizes my variables and asks for input. When I input the following values for each as a test...

V(Target speed) = 9
T (Torp speed) = 30
A (Intercept angle) = 75

...it spits out (= -0.11)
I take this to mean an 11 degree lead angle. Is that how I should be doing this?

I tried it with a different lead angle variable again to be sure.
V(Target speed) = 9
T (Torp speed) = 30
A (Intercept angle) = 135

and it spit out (=0.02). or a 2 degree lead angle
That doesn't seem right to me. Can anyone see what I've done wrong here? Is my formula off? Do I need to make the calculator see my output "Lead Angle" as an angle and not a straight number value or something?

Pisces, thanks again for the trig refresher. While I love playing this game, this has reminded me why I was a "social science" person.

What Pisces said. It appears your calculator wants radians as input. Sooo:

asin (V sin RADIANS(A) / (V ^ 2 + T ^ 2 - 2VT cos RADIANS(A) ^ 1/2)

Or something to that effect. The output of asin(whatever), may be considered a scalar. But it ain't.

Your inputs from above should spit out 17.4 and 9.9 respectively.

Now. Who's working on the Q and D spread calculator?

[Dignan]

Originally Posted by Dorjun Driver

What Pisces said. It appears your calculator wants radians as input. Sooo:

asin (V sin RADIANS(A) / (V ^ 2 + T ^ 2 - 2VT cos RADIANS(A) ^ 1/2)

Or something to that effect. The output of asin(whatever), may be considered a scalar. But it ain't.

Your inputs from above should spit out 17.4 and 9.9 respectively.

Now. Who's working on the Q and D spread calculator?

Ok, thanks. I'll see if I can figure out how to switch it to Radian output.

Before I try, doesn't putting "sin" before my A make it read that input as radians?

[Dorjun Driver]

No no no! Just use the radians() function to convert your degree input to the format your calculators sin()/cos() functions want.

While hell is breaking loose we don't want to be dividing stuff by transcendental numbers! Next thing you know, you'll want to compute just how close you can shave that shot. Anywhere in the engine room will be fine. Honest.

[Dignan]

Originally Posted by Dorjun Driver

No no no! Just use the radians() function to convert your degree input to the format your calculators sin()/cos() functions want.

While hell is breaking loose we don't want to be dividing stuff by transcendental numbers! Next thing you know, you'll want to compute just how close you can shave that shot. Anywhere in the engine room will be fine. Honest.

Ha! 10-4 on that. The calculator I'm using removes the parentheses from the sin(A) and Cos(A)when I try to save it. That seems to be my problem. I'll putz with it some more. Thanks

[Pisces]

To switch between degrees and radian and gradians on a Casio you have to press the mode button and then 4, 5, or 6. See the legend under the display.

Your inputs from above should spit out 17.4 and 9.9 respectively.

Agreed. If you get a number like 0.11 as a result for degrees, then it will infact be 0.11 degrees, NOT 11.

If it was a logarithmic sliderule then that decimal point fudging might make sense. But that method doesn't hold with a digital scientific calculator.

[Pisces]

Oh yeah, I forgot to add:

Dorjun Driver's formula can be significantly simplified if you know the AOB:

Deflection = arcsin ( Vship * sin AOB / Vtorpedo)