Optimum Cargo Extensions per TS. AKA the best bang per $.

[The_T]

The Optimum Number of Cargo Extension for a Transport Ship

Because the cost of a cargo extension increases as more are bought, there becomes a point where it is not economical to buy more cargo extensions. The optimum number of extensions is that at which The total cost of the ship, divided by its cargo space, yields the lowest possible number. As both of those increase at different rates, it is impossible to just guess where the 'golden number' is.

So, I did the math. For a ship equipped with max engine extensions, one 1mw shield, SETA (just cause), nav soft 1, and trade soft 1 and 2, the optimum numbers are as follows. The first number (X) is that golden number of cargo extensions, the second number (C) is the resulting cost per cargo space for the ship. If you equip your ships differently than I have stated above, these numbers will change, formulae are provided at the bottom that allow you to enter different set-up costs. Although you'll need either math skillz or a graphing calculator to solve them.

Mercury: X=123, C= 148.51
Dolphin: X=84, C=97.14
Caiman: X=209, C=242.55
Demeter: X=83, C=136.95
Vulture: X=70, C=91.10


And now for the math!

A simplified version of the formula I used is as follows:
C= (Total ship cost)/(Total Cargo Space)
or:
C = (I + T)/(X+Ic)

Where
C = Average cost per unit cargo space, the winning number is the lowest
I = Initial cost of ship
T = total cost of X cargo extensions
X = number of cargo extensions
Ic = Initial cargo space for ship

Now then, I and Ic are different for every ship. I is the sum of the price for the 's' version of the ship, max engine tunings for the ship, SETA, nav soft 1, and trade soft 1 and 2. Ic is the initial declared cargo value for the ship, with 0 cargo extensions

So the values of I for each ship are as follows:
Mercury: 141 923
Dolphin: 197 793
Caiman: 169 372
Demeter: 141 923 (note, this is the same as the merc)
Vulture: 148 468

And the values for Ic are:
Mercury: 900
Dolphin: 2000
Caiman: 600
Demeter: 999
Vulture: 1600

Possible values of X (number of cargo extensions installed) are also different for each ship. For the Mercury, Caiman, and Vulture, they are integers between 0 and 900, for the Demeter, between 0 and 666, and for the Dolphin, between 0 and 1000.

So that leaves the formula mostly filled out, the only remaining variable is T, or the total cost of X cargo extensions. As many people have remarked before, the price of extensions is an aritmatic series (increments by a given amount). The sum of an arithmatic series is given by:
X(A+F)/2
Where A is the initial value, always 14 in this case(the cost of the first cargo extension on all TS ships), and F is the final value, but for our purposes, this depends on X. crap.

F then, is some value, N I'll call it, (starting to run out of letters) multiplied by X with 14 added to it.
F=NX+14

what's N? It is the amount by which the price of the cargo extensions increments. Luckly, the initial value for a cargo extension is always 14, and the cost of the last extension is always 1000, so N is given by (1000-14) / Xmax [the maximum number of cargo extensions] .
There are 3 different values for N; for the Mercury, Caiman, and Vulture, N = 1.09556, for the dolphin, it equals .986, for the Demeter, it equals 1.48048.

So substituting all these values into C = (I + T)/(X+Ic) gives a new general formula of:
C= (I + X(14+(NX+14))/2)/(X+Ic)
If you care to expand this out, you will find its a quadratic function, therefore, the minimum value of the curve will give us the optimum number of cargo extensions per ship.

From this we get a different equation for each ship.
Mercury: C= (141 923 + X(14 + (1.09556 X + 14)) / 2) / (X + 900)
Dolphin: C= (197 793 + X(14 + (.986 X + 14)) / 2) / (X + 2000)
Caiman: C= (169 372 + X(14 + (1.09556 X + 14)) / 2) / (X + 600)
Demeter: C= (141 923 + X(14 + (1.48048 X + 14)) / 2) / (X + 999)
Vulture: C= (148 468 + X(14 + (1.09556 X + 14)) / 2) / (X + 1600)

What those equations do: They give the price per cargo unit of a ship, with X cargo extensions. If you equip your ships differently than I do (as described in the declaration of I, change the initial value(I), this will result in a different value of X corresponding to the minimum value of C, the higher I is, the higher X will be.

Where all this is going to. The objective was to find the optimum number of cargo extensions, ie. total ship cost/cargo space. So that means we want to find the minimum value of C for each of those equations. I do believe there are 3 ways to do this:
1. Some sort of algebraic solution, but i can't remember how
2. Calculus; Solve the equation for where the first derivative of that equation is equal to 0; Can't be bothered to do this 4 times.
3. Graph them on a graphing calculator, and find the min value of the curve: We have a winner!.

So then, the values I get are:
Mercury: X=122.78=123, C= 148.51
Dolphin: X=84.32=84, C=97.14
Caiman: X=208.62=209, C=242.55
Demeter: X=83.05=83, C=136.95
Vulture: X=70.37=70, C=91.10

Closing remarks:
As you can see, for general transport ships, it is not in your favor to buy very many cargo extensions. Your personal TS is a different story, but that's not what i'm concerned with here. It is also worth noting that the Vulture has the lowest cost of any ship per unit of cargo space, although that only gives it 1670, whereas the dolphin gets 2084 at its best. The caiman, even for a speedy ship is bloody expensive, while the demeter is, all things considered, a pretty good deal, and the merc keeps up the tradition of average argon.

[The_Abyss]

Wow.

That will certainly be useful for new players choosing their first few TS ships, but most people once they're beyond that will probably make a simple choice based on either max capacity or max speed.

I hope any new players reading it appreciate the work that went into it!!!

[AdmiralTigerclaw]

Does this take into account that a fully functional factory complex can make three million an hour? That in a six hour period you can make more than enough to compensate for whatever costs you have? OR that any player with admiral rank or better can take an assassination mission and make twenty mi ill ionon o and make the whole chareta o-bsoloeetete?E???????
'

*Gets a derranged and insane grin as he sits at his keyboard, handsss shaking violently like a madman. Then gets up and grabs a Jolt Cola*


Okay, I'm better now. *Twitches slightly.*

Seriously, did you have to do all that math? It's been two years since I've done hardline math...

[The_T]

Abyss; Thank ye sir.
Tigerclaw;
question 1. no, obviously not, don't be a retard.
question 2. yes, i did have to do all that math, and I did it to see if i could. I like challanges.

[AdmiralTigerclaw]

*Brain throbs in pain...*

The numbers... THE NUMBERS!!!

Anywho... can you simplify that, or at least make it a visual graph. Some players may be daunted by the many numbers and formulas. (I can get them, but only if I click on the math processor laying dormant in my skull.)

[softweir]

Very interesting!

I would advise players to be careful about applying these results too rigorously. It would be tempting to buy several optimally expanded Boron Dolphins to, for instance, sell the produce from an SPP. However note that these may be significantly less profitable than one large Dolphin, due to the way the price at a destination station drops when a half-expanded Dolphin sells its cargo, leaving the next Dolphin with a much poorer selling price.

Similarly, a Universe Trader's ability to carry several cargos at once would be rather compromised!

However, for many purposes it is worth being aware that a fully maxed TS is far more than is necessary.

[pocket247]

Thats a lot of info there, which is pretty useful for a persons first TS. Its cool to see that some ppl are prepared to spend time to work these things out.
For me though, I've always stuck with Demeters (for their excellent speed/cargo/75MW shields) for everything, except crystal buying runs (maxed Iguana's for that), and Energy selling (maxed dolphins, except in dangerous areas, which I use Demeters again).
I guess my point is, that although some ships, like the Vulture, may appear very good from a cargo/price relationship, it may not be the best option for total functionality. For me, a TS, is a tool.
E.G. it must take goods from A - B, so perhaps some adjustment for speed (and also, perhaps, how much it costs to achieve max speed) should also be included as well. A TS ship isn't something that sits in a docking bay to be admired (none of them are particularly pretty are they), but are used to transport goods.
Excellent work!

Cheers,

Pocket

[Aye Capn]

Well done, The_T, very well done.

My own "formula" is to buy extensions up to the 400 cr price point, which I figure means the extension "pays for itself" after 40 ecell runs.

However, I've gone extravagent on UT extensions, the idea being they'll do hundreds of cargo runs over their lifespan. Your calculations lead me to think perhaps that is a big mistake: more UT's with smaller cargo bays seem like a smarter investment.

[The_T]

Thanks for the complements folks.
Tigerclaw: I can't really simplify it beyond what's there, to simplify the math... if somebody with better algebra than I would like to have a go at cancellling out as much as possible, than be my guest, but it will still just give another form of the same equation. Graphically, its a quadratic... (I think anyway, looks like one, i guess it could be hyperbolic though ) That is to say, on a graph, it takes the shape of a 'U' I was looking for the lowest point on that U.

Softweir, that's exactly right, its a good idea to install extra cargo extensions in your selling ships especially, but not to many. however, for delieveries between your own stations, for looping etc, it makes sense to be as economical as possible. If a vulture with 70 cargo extensions can keep a loop running at full capacity, then why buy something else?

Pocket; I considered adding speed in, but wasn't sure how to do that, and whether it would make much of a difference. I suppose if you divided the C values by speed, you'd get price per unit cargo per meter per second... uhhh....yeah.... so in other words, the data is up to everyone's own interpretation.

Aye Capn; Thank you,
as for the cargo extensions for UTs, you should actually buy more. This is because the amount of credits you put into a UT is 5 to 10 times what you put into a standard interstation TS. For all UTs, you need to add trade mk 3, at 501 340 credits, fight soft 1 and 2, about 6000 credits, a jump drive, 101 072 credits, a laser, say a gire at 6000 credits (I don't have all the numbers in front of me obviously) and some 25mw shields, 185296 each, I'll crunch the numbers for a dolphin, and say we have 3 shields. our new initial price is now 1 363 041. And we start with 30 less cargo space for the shields.

The X for this is 597 cargo extensions, at 602.69 credits per unit of cargo space.

Also, I do beleive that UTs upgrade the cargo space on their ships to 75% by themselves anyway, so its pretty much a mute point. You might even want to start them off at 75% (so 750 extensions for a dolphin) this will increase their leveling.

[AdmiralTigerclaw]

I know enough math to understand Quadratic and Hyperbolies... I just want a flat assessment. Just I want something that doesn't need three paragraphs to explain all the little things, just the important points.

There are just days I don't want to sift through it all to get to the point.
I understand the whole thing perfectly.

At least it doesn't involve SINE functions and other fun bits like that. Then you'd REALLY lose people.

[The_T]

alright, if you equip a ts with max engine tunings, trade soft 1 and 2, nav soft 1, and one 1mw shield, you should install the following number of cargo extensions on ships, especially if you're using them to move goods between your stations.
Mercury: 123
Dolphin: 84
Caiman: 209
Demeter: 83
Vulture: 70

That about what you want?

[AdmiralTigerclaw]

This all makes them have the same amount of cargo space yes? Or explain why I should install that number...

[esd]

Basically beyond that point it begins to be cheaper to just buy another ship.

[The_T]

This all makes them have the same amount of cargo space yes? Or explain why I should install that number...

yes, like esd said, don't buy more than that, just buy another ship, I'll try to explain why as best I can.

You have noticed that as you add cargo extensions, they become more and more expensive correct? for example, the first one only costs 14 credits, great! buy it! but the last costs 1000 credits, not so great is it. Well, it makes a lot more sense to have three dolphins with no cargo extensions which can, together, carry 6000 units of cargo and will cost under 600 000 credits than to have 2 with 1000 cargo extensions, which would costs over a million credits but can also carry 6000 units of cargo. However, up to a certain limit, it actually makes sense to add cargo extensions, your ships will essentially carry more for less, but add to many, and they carry more for well... more. That transition is the numbers that I came up. Unfortunatly, those numbers depend on several different variables that the math has to account for, so it got somewhat complicated.

[softweir]

One problem with applying these formulas to UTs - the damn things use Energy Cells PER JUMP, regardless of expansion / cargo volume. Therefore, having twice as many UTs each with half the cargo space will (for the same transfer of cargo) cost twice as much in terms of energy cells. Eventually this energy cell cost will exceed the difference in setup cost.

I assume that UTs are highly unlikely to be destroyed. If they had a limited lifespan then the additional replacement cost of a fully-expanded UT would factor into the equation and outweight the energy cell consumption saved.

(I have had 8 UTs running for a great many hours gametime, and have yet to even be told of one being under attack. They have never taken any damage. [Do they avoid HENs?])

[AdmiralTigerclaw]

This also depends on if I'm going for straight cost effectiveness VS cargo efficiency.

Two dolphs with partial cargo upgrades VS one maxed out dolph. Logisticly, two dolphs mean two seperate vehicles to keep track of, and where applicable, defend. If I use the one dolph as a hauler... I usually intend to maximize its capacity, especially when hauling ORE because of the volumes I need to transport. With two haulers for ORE, they may conflict with each other when one pulls part of the supply from its production, and the other rerouts to nearby facility a sector away, killing time, and production effeiciency.
The way I see it, I can buy a ship, max it out, and more easily defend it, track it, and save on efficiency by picking the ship for the task. In this way, for hauling ORE or other bulk shipments en MASS, nothing less than a maxed transport will do. Remember the rule of bulk purchasing. The transportation may be expensive, but the return for value rate makes up for it.

[[RFA]Gravity]

Ok i just skimmed the first post, i mean hell does everyone need a degree in maths here or something

[[RFA]Gravity]

Also has anyone noticed if your a bit strapped for cash and your setting up a factor the express is a far more economical transport than the mercury as it is faster, it has more space (for us cash strapped people) buying cargo upgrades is an expensive business and it can be used to ferry products up to size L so if they are XL e.g silicon then a mercury has to be used.
Due to this the number of argon expresses far outnumber the number of mercuries in my fleet.

[Pirate Hunter]

I will add this to the guide.

Good post for newbies that are straped for cash. I made the mistake of Full upgradeing mercs to sell my E Cells this post would have been handy for me.

Alough I may have to get a A level in Maths to understand it

[[RFA]Gravity]

ive got an A-Level and im struggling with it