You did take into account that they accelerate for half the journey, then de-accelerate for last half, right?
People do tend to forget that to stop you need the same output only in reverse....
I was never any good with distance over time and acceleration calcs in high school, so I have no idea what those numbers mean.
Yep. That is the Brachistochrone equation and basically it tells you how long it takes go from A to B (or rather cover distance D) given constant acceleration while factoring in the need to decelerate.
It's derived from basic equation you'd have seen in high school physics, and Calculus: X = 0.5at^2 + ut + c
Right you are! I used the same method but lost a /2 in my math.

So even faster. Good to know.
Heh. That's why I basically always write out the math while posting. That way people can point out when I make stupid mistakes like that.
Also can you get me a company value estimate for Shifting Developments (It's being bid on).
Sure thing.
Ownership is mostly held by five people.
Not really sure on the shares thing. ~80-90% are in the hands of the founders
This right here says that the sale price isn't going to match the valuation of the company but more what the owners think they can get for it. This can be a pretty major swing factor depending upon the people involved and their relationships but I'll cover that in a bit. We can basically ignore the effects of anyone other then these five people.
No real profit they've spent the last year and a half developing a product (Vehicle scale ammo mods)
Debt to equity is probably fairly good, but they are a new startup
So it's essentially a brand new company with a nifty product. The fact that they actually have a good Debt to Equity ration, rather rare for a new company (especially one that has been running for a year and a half with no profit), is surprising.
This suggests that the owners are rather wealthy and really dedicated to their company if they were willing to pump in the kind of cash we're talking about here. Even with just one science team in a Lab I they are looking at a
minimum of 25 million and more likely in the 30 to 40 million range.
Really looking over the information the company is basically worthless. It's just like every other startup small business, which with an 80% failure rate within the first three(?) years aren't a very good investment. The only thing that makes it valuable is the patent rights to their vehicle mods.
So it really comes down to two factors:
1) How much the vehicle mods are worth?
I can't really give a hard number here but this is big. Like waaay big. Phasic rounds will make ships a lot more vulnerable since even with a 50% damage reduction a single round is going to basically obliterate anything it hits. Incendiary rounds would be useless in space but depending upon how the KBs are set up Cryorounds would be devastating as would Shredder rounds (big issues with Railguns is over-penetration).
They don't have the full set yet but what they have is pretty nasty. Depending upon the cost the moding tech could be worth hundreds of millions to out right billions of credits.
Especially since no one is going to be able to (legally) replicate them for quite a while. (see later on)
2) How willing the owners are to sell?
These guys have poured a lot of time and money into creating Shifting Developments. This suggests they knew they had a winning idea and just needed the numbers to make it work or they really believed in this product.
In the first situation they'd likely sell out for as much as they can get. In the latter well they aren't going to be selling out. The only exception is if one of the five owners is really a venture capitalist rather then a 'owner' since they'd be most interested in ROI and frankly SD would likely struggle to bring these mods to the market by themselves. So any 'sane' venture capitalist would want to sellout now.
There's a few large companies willing to bid a pretty penny to get ownership, but after a point it just becomes cheaper for them to develop the product on their own.
That point is going to be pretty high since
if SD have patented their stuff properly it wouldn't be the actual mods they patented (well it wouldn't just be the mods) but also the way of getting infantry mods to work with larger weapons.
It's a novel invention and wouldn't fall under the public domain like "squareness" does. So unless these other companies can find a different way of making mods work with big guns (unlikely without a
lot of time and money) they won't be able to for the next ten or twenty years (depending upon patent life in ME). If they haven't patented it properly (or
at all!) then the value drops significantly.
So I need a value for the bids.
Pretty arbitrary since the company by itself is basically worthless but I'm figuring somewhere in the range of 100m to 10b sounds about right.
100m would be the opening offer level while 10b would be the walk away and figure it out yourself threshold.
Spaceship companies are going to want this the most but even companies dealing primarily with planetary vehicles are going to be interested. Space companies would probably go all the way up to* 10b depending upon their specifics while most planetary companies wouldn't like enter the billion range*.
It will likely only be large companies like CHA and HK bidding because they are the only ones with the raw scale to take full advantage of the mods. They also benefit since depending upon the monopoly laws (too late at night to contemplate them) they could get away with only making
their stuff compatible with the mods which would increase the value of all their combat capable vehicles.
I could be off however. It all really depends upon whether these vehicle mods are as much of a game changer as I think they could be since that is the primary value source for the company.
*People can be very sensitive to range jumps. Going from 999m to 1,000m is often harder for people then going from 900m to 999m despite it been a larger jump. That's why things are always for sale at xx.99 or xx.95
If you can get a estimate to me quickly then that'd be awesome but if not I can delay the voting on it for an update.
Hope this helps.