Define a hover + cruise mission and size the pack it needs — every number recomputes as you type, right here in the browser.
Preliminary momentum-theory model. Need wing loading, propeller, stall/AoA, moment or full trim analysis too? The rest of the suite is still available in the full calculator app while it's converted over one dashboard at a time.
One physics chain runs the whole page — mission → thrust → power → energy → capacity → weight — using actuator-disk (momentum) theory for hover and a two-force trim balance for cruise.
Hover thrust is set by a single coefficient, the thrust-to-weight ratio kT/W (the slider above), defined as the surplus of thrust over the vehicle's own weight:
kT/W = 1 would exactly cancel gravity and nothing more — the vehicle could hover motionless but couldn't climb, correct its attitude, or reject a gust; any disturbance and it starts falling. Everything above 1.0 is the real "flying margin": climb rate, pitch/roll control authority, and gust rejection. In practice kT/W ≈ 1.2–1.5 covers a gentle hover-capable multirotor, rising to ~2.0+ for an aggressive or wind-tolerant design. Rearranging for the thrust each rotor must produce:
Cruise thrust is not just drag unless the vehicle is flying perfectly level. This is a tail-sitter — the rotors are fixed to the airframe, so thrust always points along the body, at pitch angle γ from horizontal (γ = 90° in the hover leg above, γ = 0° would be a fully level cruise). At any γ > 0°, thrust has to do two jobs at once: push against drag and help the wing carry weight, because the wing only sees the lift it's given at the flown angle of attack:
Resolving forces along and perpendicular to the flight path gives two conditions thrust must satisfy simultaneously. With one number (T) and two conditions, the harder of the two sets the requirement — exactly the same "whichever binds" logic used for the battery itself in step 4 below:
At γ = 0° the second condition drops out (sinγ = 0) and this collapses back to the familiar T = D. As γ grows, gravity leaks into the along-path equation (W·sinγ) and the wing's lift covers less and less of the weight, so required thrust climbs — sometimes sharply — above simple drag.
Each rotor holds itself up by throwing a column of air downward through its disk area A = π·D²/4, at an induced velocity v — the speed of that air right at the disk, in m/s:
That factor of 2 is easy to doubt but it's not optional — it falls straight out of actuator-disk (Rankine–Froude) momentum theory, and the reason is that v and w are two different speeds. v is the air's speed right at the disk; w is its speed once it's settled into the fully-developed slipstream, further downstream. The disk creates a jump in pressure, not in velocity — so the flow keeps accelerating for a while after it passes through, driven by that leftover excess pressure, until it reaches w far behind. v and w are related by requiring two different ways of computing the disk's power to agree: from momentum, power = T·v; from kinetic energy gained by the flow (starting at rest), power = ½·ṁ·w². Since thrust itself is T = ṁ·w, setting the two power expressions equal and cancelling terms gives:
So the induced velocity at the disk is exactly half the far-wake velocity — not a rounding choice, a consequence of momentum and energy having to describe the same flow consistently. Thrust comes from accelerating the mass flow ṁ = ρ·A·v from rest up to that far-wake speed w = 2v, not just up to v:
(Skip that factor and you're implicitly claiming the disk accelerates air to its final speed instantly at the disk itself, with no wake left to contract — that's the mistake the "no 2" intuition falls into.) Ideal power is thrust acting through the velocity at the disk, v:
Real rotors lose more to blade drag, tip losses, and motor/ESC inefficiency — lumped into η:
Cruise power is simply the trimmed cruise thrust from step 1 times cruise speed V [m/s], marked up the same way:
Each mission leg's power is sustained for its own duration, then summed:
A pack stores E = C_Ah·V_nom (V_nom = S·V_cell), and only a fraction (DoD) is usable — so it must hold more than the mission needs. It must also survive the peak segment's current draw within its C-rating; whichever limit is harder sizes the pack:
From the cells' specific energy (Wh/kg):
Long, gentle missions come out energy-limited; short high-power ones come out current-limited — the result panel flags which one binds. This is a lumped-efficiency momentum-theory model with no mass feedback loop: the pack weight is an output, not fed back into the thrust calculation, so check the "% of assumed mass" note and adjust the mass input if it's far off.