Rocket Lab: Δv
Getting to orbit is a budget problem, not a power problem. Set your dry mass, fuel load, and engine, and the Tsiolkovsky equation tells you how much velocity you can buy.
Vehicle
Trajectory
ballistic arc
Delta-v budget — what your design buys
Lawn dartset some fuel and try again
How this works: the controls feed the Tsiolkovsky rocket equation: delta-v equals exhaust speed times the natural log of wet mass over dry mass. The equation above the meter shows your own numbers going in. The meter is banded: below 9,400 m/s you come back down, above it you are in orbit, and past 12,690 m/s you leave Earth for good. Those figures include drag and gravity losses. The trajectory panel is schematic and not to scale.
Why fuel gives less than you expect
The rocket equation has a logarithm in it, and the logarithm is the whole story. Your delta-v depends on the ratio between your fueled mass and your empty mass, not on the amount of fuel. Doubling the fuel does not double the speed, because the extra fuel has to be carried and accelerated by the fuel beneath it. Each additional unit of velocity costs more mass than the last one did.
That leaves two real ways forward. Raise the exhaust velocity, which is what a better engine means: an ion thruster with an Isp near 3,000 seconds sips propellant, but pushes so gently that it only works once you are already in space. Or throw away structure as you climb, which is what staging does. Every orbital rocket flying today is a stack of tanks designed to be dropped, because the equation punishes carrying anything you no longer need.