In alpha and beta versions of Minecraft (prior to Minecraft Beta 1.6), 'Minecart Boosting' takes advantage of the minecart's physics when next to another cart to propel itself forward.
How many vertical blocks can a cart climb per square of booster track, assuming the cart goes straight up after leaving the booster area?
What's the minimum length required to go all the way from bedrock to cloud level?
Minecart boosting was removed in Minecraft Beta 1.6.
This answer is only relevant for versions of Minecraft built prior to that revision, accessible using the Minecraft Launcher's Time Machine functionality.
It depends on whether the cart has a rider (cow, chicken, player) or not.
Now, first some definitions. The type of booster used is a speed and momentum resetting booster, to ensure fair and reproducable results.
This is a booster with a length of 1
and here a booster with length 11
The bottom bedrock layer shown in these images is layer 0, the void is directly below. the track going up shown on the left side is the actual track going up.
The results are in and show that an empty cart needs a booster of 18 long, while a cart with a rider in it will need a booster of 5 long to reach beyond the top of the map. (altrough, a booster of 17, with an empty cart, reaches sufficiently close.)
Now, for the booster lengths below these numbers, the following results has been obtained:
Raw data (height reached, booster length is position in list, where the first has a length of 1 as shown above.):
empty cart: 6 12 17 25.5 31 41 47 57 63 72.5 79 88 93.5 103 109 119 125with rider: 6 25.5 37 66I'm now trying to make some sense of the results for the empty cart, I don't think I have enough data points to make something for the cart with a rider.
I do not know the answer to your main question, but what I do have to offer is some insight on the difference between speed and momentum.
In minecraft, there is no real maximum momentum. Your speed is capped, but your momentum is not. As you continue boost the same minecart, it will not get any faster, but it will continue to gain momentum. This increased momentum will allow it continue going at the maximum speed for a longer time before you need another booster or downward slope to continue.
However, if you increase the momentum of a minecart too much, the game is prone to crash, so you have to be careful when doing this as well. Reaching maximum speed can be done with an extremely short booster, but the length of the booster will still affect how far you are able to go because a longer booster will result in more momentum.
Booster Article on the Minecraft Wiki.
In my very brief testing, a cart that was boosted for a single track section only made it up eight vertical blocks (on a 1x1 staircase). Increasing the boosted track to two sections improved the climb to 28 blocks.
