solar panel tilt depending on latitude
What you are looking for is called the "Solar Declination Angle". Basically this tells you the maximum angle the sun will reach at the equator on a given day of the year. This value will vary between the two tropics (\$\pm23.45^\circ\$) depending on the time of year - because of the tilt of the Earth and how that relates to the sun.

If we take a line which is perpendicular to the Earth's axis of rotation (basically any line which runs from the centre of the Earth through any point on the equator), we can calculate the solar declination as:

$$ \delta=\mathrm{sin^{-1}}\left(\mathrm{sin}(23.45^\circ)\times\mathrm{sin}\left(\frac{360^\circ}{365}(d−81)\right)\right) $$

Where \$d\$ is the day of the year (1 = January 1st, and 365 = December 31st), and \$\delta\$ is the solar declination relative to the equator [1].

Now from this you can calculate what angle to place your solar panel at. Essentially you want its normal (the line perpendicular to the surface of the panel) to be at \$\delta^\circ\$ relative to vertical at the equator (\$0^\circ\$ latitude). Now to get this angle you will have to factor in your latitude which is essentially an offset of you relative to the reference frame the above calculation is in.

So the tilt angle becomes:

$$\theta = \phi - \delta $$

Where \$\phi\$ is your latitude in degrees, and \$\theta\$ is the tilt of the panel in degrees between its normal and straight up at your latitude. That is basic geometry, but you should double check the meaning of +ve and -ve angle, I can draw up a diagram later if you need clarification.



As a side note, it may be worth adding that the reason for subtracting 81 in the solar declination calculation. Basically the maximum value of \$\delta\$ occurs around June 21st which is day 172. The maximum value of the sin function occurs at 90 degrees. Subtracting 81 gives us 91 for that day which happens to be roughly 1 quarter of a year:

$$\mathrm{sin}\left(\frac{360^\circ}{365}(172−81)\right) = \mathrm{sin}\left(360^\circ\times\frac{91}{365}\right) \approx \mathrm{sin}\left(90^\circ\right)$$



Source [1]: PVEducation.org - Declination Angle