I attempted to work this out in excel. Is this correct?
As far as I can tell, what you have is not correct. There are a number of issues
1) Rather than picking A = 10 and B = 10 specifically, if you're going to work it out numerically using Excel anyway, you
could actually just plug in all the values for the constants that make up A and B in the original problem. However, since you're just looking to figure out the
shape of the function for now, to see how it varies with phi, picking arbitrary values like A = 10 and B = 10 is ok as a start.
2) The shape of your function looks wrong. It's monotonic (which means steadily increasing or decreasing). That is very suspicious, since both cosine and tangent are periodic functions, so I would expect your answer to have some sort of cyclic variation (or at least some sort of variation up and down). I suspect the problem is one of
units. Phi seems like it is supposed to physically represent some sort of angle. And, based on the fact that you are plugging in values for phi like 90 or 100, I'm guessing you are choosing phi to be in degrees. But you have to remember that an angle in degrees is never what goes into a trigonometric function. Plugging in an angle in degrees into cosine or tangent is nonsense. Those functions take dimensionless numbers, which means that the angles you plug into them have to be in
radians. I doubt very much that you intended to plug in 50 radians or 100 radians, since radian values are redundant outside the range of 0 to 2*pi. Convert your angles to radians first.
3) There is also the B*phi term, which is not a trig function. What units of phi is it expecting to be plugged into it? Well, it's
unclear. It depends on the units of all the constants that go into it. If all those constants have units of C_limb, then phi needs to be a dimensionless number, and therefore should be in radians. This seems like the most likely case to me. However, if all those constants multiply together to produce something that has units of C_limb
per degree, then the expression is obviously expecting phi in degrees. The point is,
you have to figure that out based on your knowledge of the physical constants.
4)
Even if I plug in phi in degrees into the expression (which I want to emphasize, is the
wrong thing to do), I don't get the same numerical values as you, which leads me to believe you might have an error in your Excel formulas. I get these numbers here:
10 [ 81.45528447]
15 [ 177.5205456]
20 [ 302.42816687]
25 [ 254.67280289]
30 [ 305.99248256]
35 [ 321.74127835]
40 [ 422.98985998]
45 [ 572.96044153]
50 [ 504.35150848]
55 [ 550.76767057]
60 [ 553.17024555]
65 [ 669.68816588]
70 [ 853.03171688]
75 [ 754.03089215]
80 [ 796.4806867]
85 [ 755.63966519]
90 [ 917.17522733]
95 [ 1149.5590293]
100 [ 1003.70540446]
105 [ 1042.74292698]
Note, also, that this wrong function is not monotonic either. it has lots of negative spikes. it just happens to always be positive for these input values.