I drew up an example to help myself understand what the module would do in action.
I've selected 35 degrees since it's midway between the speed where a catapult is initially affected (25 degrees) and where it would stall (45 degrees) so it will move at half speed - see here for more info
http://mwomercs.com/...ement-behavior/
In this case the vertical displacement is 25m *sin(35 degrees) = 14.34m
This makes the face of the hill 28.82 metres in length from the bottom to the top.
The catapult is initially moving at 80 kph (22.2222 m/sec) and will decelerate to half that (11.1111 m/sec) over a certain distance.
Using d=v1t+1/2 At^2 we can calculate this distance.
Without Module:
Without the hill climb module installed, t is 1.0 so A=(11.111-22.222)/1.0, or -11.111m/s^2
d=22.222-5.555
d=16.666 metres up the hill before we are moving at 40 kph.
This means the remaining 12.154 metres (28.82-16.666) will take 12.154/11.111 =1.094 seconds
The total time to get to the top is 2.094 seconds!
With Module:
Without the hill climb module installed, t is 1.1 so A=(11.111-22.222)/1.1, or -10.101m/s^2
d=24.444-5.051
d=19.394 metres up the hill before we are moving at 40 kph.
This means the remaining 9.427 metres (28.82-19.394) will take 9.427/11.111 =0.848 seconds
The total time to get to the top is 1.948 seconds!
So for 15,000 GXP and millions of cbills, and a module slot
you can get up there 146 milliseconds or ~6% faster you lucky so and so.
Bonus round! What happens if the catapult starts half way up a hill?
Let's imagine a scenario where you're on an island, watching the enemy changing position over time (e.g. crimson strait). You have managed to get yourself a nice ridge to watch from on the side of a hill with some cover, but you do not have jumpjets so you have to walk up and down to take shots and return to cover. Does the hill climb module help us prevent the enemy freely changing positions?
Sadly no, pro-mctagonist is initially stopped, so the hill deceleration module does nothing in this scenario.
So in short, it's more of a hill charging module than a hill climbing module. It will (ever so slightly) improve how fast you can charge up a given hill, but it won't actually make your climbing abilities any better if you ever stop.