KerbNet: FoV, altitude, and area/dimensions

[ajburges]

Does anyone know an equation relating FoV, altitude (or orbital radius), and KerbNet map dimensions/area? I want to make a calculator for different anomaly "scanner" orbits, but I know there is some anomaly in the equation to make surface scanners work nice landed.

Edited March 25, 2017 by ajburges

[bewing]

They just switch modes when landed to give a bigger FoV.

AFAIK, the equation should be: Kerbnet width = 2 * altitude / cos (FoV)

Edited March 25, 2017 by bewing

[ajburges]

56 minutes ago, bewing said:

They just switch modes when landed to give a bigger FoV.

AFAIK, the equation should be: Kerbnet width = 2 * altitude / cos (FoV)

That doesn't make any sense. There is a asymptote at 90° in that equation as cosine approaches zero.

The equation for linear FOV as a function of angular FOV is:

2*distance*tan(FOV/2)

If that equation is indeed correct, does that mean the higher you mount a Probodobodyne RoveMate the further it sees? I could swear the low placed body of a simple rover could scan further than the  458.4 m a 1 m height would allow.

[bewing]

13 minutes ago, ajburges said:

There is a asymptote at 90° in that equation as cosine approaches zero.

OK, I guess I should have said FoV/2. Yes, there is an asymptote at FoV/2 = 90 degrees. You only get the FoV mode switch for landed probecores. If a landed probecore is on a 3-meter-tall rover, it will indeed see farther than one that's mounted 1m above the terrain. As soon as you pop up into the air, the FoV instantly gets reduced to a much smaller value.

 

[ajburges]

 

20 hours ago, bewing said:

OK, I guess I should have said FoV/2. Yes, there is an asymptote at FoV/2 = 90 degrees. You only get the FoV mode switch for landed probecores. If a landed probecore is on a 3-meter-tall rover, it will indeed see farther than one that's mounted 1m above the terrain. As soon as you pop up into the air, the FoV instantly gets reduced to a much smaller value.

 

 

I just tried a multi-core tower. The different core heights do not affect KerbNet results. All cores must use a fixed point WRT vessel for altitude.

Having the equation use csc instead of tan still does not make sense. The altitude represents the adjacent side, not the hypotenuse. You inaccuracy would increase as you reduce angular FOV, with asymptotic behavior at 0! (Since tan is 0) As I want this to solve for a narrow aperture, that inaccuracy is bad.

I may loose interest in mathematically solving this soon. I just researched how to generate a rational approximation of irrational numbers (for orbital resonance) and don't currently have a though as to how to implement it in a google sheet. Still considering alternate calculation paths.

[ajburges]

Lacking an answer I took some measurements from a conveniently located "perfectly" equatorial station using KerbNet. The data sucks!

Latitude and longitude are degrees so ground distance is approximately the ratio of circumference of the 6e5 m radius Kerbin. Arcs are measured from center to bottom left (retrograde, anti-normal) corner and doubled.

fov (°)	lat/long delta (°)	arc distance (m)	chord length (m)	alt (m)	lin fov formula (m)	(err vs arc)	(err vs chord)
9	1.183	24783.7	24781.9	168037	26449.6	6.72%	6.73%
9	1.183	24783.7	24781.9	168037	26449.6	6.72%	6.73%
45	6.533	136833.8	136537.5	168050	139217.2	1.74%	1.96%
45	6.883	144164.2	143817.7	168050	139217.2	-3.43%	-3.20%
81	17.433	365122.9	359515.1	168040	287039.4	-21.39%	-20.16%
81	18.317	383623.4	377122.3	168040	287039.4	-25.18%	-23.89%

The formula is almost in the right ballpark but the error behavior makes no sense. I could understand a linear error function (as you can't target the true edge of the window), but this small data-set suggests the default FoV was most accurate. The csc formula was ludicrously inaccurate.

Edited March 29, 2017 by ajburges

[ajburges]

Okay, I managed to write my own Sheets function to generate Farey ratio approximations. Then I learned that generating orbits from a desired ratio makes more sense. 

Still wondering what I am missing for a more accurate linear FoV equation. Unless I can get that, I am left having to adjust orbit until I stumble into one with the correct linear FoV and resonance.

Edited April 6, 2017 by ajburges