Why short verticals need a coil
A vertical less than a quarter wavelength long has a capacitive feed impedance. A loading coil adds the matching inductive reactance to cancel it, so the antenna resonates. The calculator uses the transmission-line model of a short monopole: the length above the coil sets how much reactance is needed, and the length below shifts it.
Base, centre or top loading
Where you put the coil changes how well the antenna radiates. With the coil at the base, the current falls steadily up the whip. Moving the coil up keeps the current high along the lower section, which raises the radiation resistance and the efficiency, although the coil then needs more inductance. Centre loading is the usual compromise on mobile whips. Try changing the lengths to see the effect.
Efficiency
A short vertical's radiation resistance can be only a few ohms, so coil loss and ground loss eat a large share of the power. Use thick wire, a large former and space the turns slightly to raise Q, and give the antenna the best ground you can. The efficiency figure includes both. Wheeler's formula gives the turns for a single-layer air coil, assuming close winding. Expect to trim the coil a turn or two with an analyser.
For full-size verticals, use the quarter-wave vertical calculator, and for other coils, the coil calculator.
Questions
What is a loading coil?
An inductor in series with a short antenna, which cancels its capacitive reactance so it resonates at the operating frequency.
Is centre loading better than base loading?
Usually, yes. It raises the radiation resistance and efficiency, though the coil needs more inductance.
How efficient is a mobile HF whip?
On 40m and 80m, often only 5 to 20%, because of low radiation resistance and losses in the coil and the car's ground. On 10m and 20m it's much better.
Why is my coil's resonance off?
Stray capacitance, the whip's real diameter and nearby metal all shift it. Trim the coil or the whip length with an analyser.