Formula Card

Every formula the handbook derives, on one page — each with the reference build's value so you can sanity-check your own arithmetic against a known-good answer. Derivations live in the linked modules; this card is for the field and the spreadsheet. (5″ reference: 650 g, 6S, 1855 KV, Gemfan 51466 — the build page assembles it.)

Lift & power — Module 2

Formula	Answers	Reference build
$\text{TWR} = \dfrac{T_\text{max}}{m\,g}$	Can it accelerate? (freestyle: 8–12)	$6000/650 = 9.2$
$\text{throttle}_\text{hover} \approx \sqrt{1/\text{TWR}}$	Where hover sits on the stick	$\sqrt{1/9.2} \approx 33\ \%$
$P_\text{ideal} = \dfrac{T^{3/2}}{\sqrt{2\rho A}}$	Momentum-theory floor for hover power	$\approx 46$ W ideal → ≈ 122 W real at the battery
$T = C_T\,\rho\,n^2 D^4$, $P = C_P\,\rho\,n^3 D^5$	Why big slow props win on efficiency	thrust ∝ RPM², power ∝ RPM³

Motors — Module 5

Formula	Answers	Reference build
$\text{RPM}_\text{no-load} = KV \times V$	Top of the rev range	$1855 \times 25.2 \approx 46\,700$
$K_t = 9.549 / KV$ (mN·m/A)	Torque per amp — predicts current	$\approx 5.15$ mN·m/A
$v_\text{pitch} = \text{RPM} \times \text{pitch}$	Hard upper bound on speed	$32\,700 \times 4.66''\approx 232$ km/h (real: 130–150)

Energy & endurance — Module 6

Formula	Answers	Reference build
$E = V_\text{nom} \times \text{Ah}$	What actually flies (energy, not capacity)	$22.2 \times 1.3 = 28.9$ Wh
$t = 0.8\,E / P_\text{avg}$	Honest flight time (80 % usable)	11.4 min hover; 3–5 min freestyle
$\Delta V = I\,R_\text{int}$	Punch-out sag on the OSD	$120 \times 0.021 = 2.5$ V
$P_\text{heat} = I^2 R_\text{int}$	Why packs land warm	$\approx 302$ W inside the pack
$m_b = 2\,m_0$	Endurance-optimal battery mass	derivation in Module 6; plateau is wide

Radio link — Module 1

Formula	Answers	Reference numbers
$\text{FSPL} = 32.44 + 20\log_{10} f_\text{MHz} + 20\log_{10} d_\text{km}$	Free-space path loss	2.4 GHz @ 2 km ≈ 106 dB
margin $= P_\text{tx} + G_\text{ant} - \text{FSPL} - S_\text{rx}$	Will the link hold?	≈ 26 dB at 250 Hz (Receiver)
every −3 dB sensitivity	≈ 1.4× range	250 Hz → 50 Hz ≈ 2× range

Tuning & filters — Module 9

Formula	Answers	Reference build
$f_\text{motor} = \text{RPM}/60$	Where the spectrogram ridge sits	300 Hz at hover → 533 Hz full throttle
blade-pass $= f_\text{motor} \times$ blades	The second ridge	900–1600 Hz (3-blade)
$t_d = \dfrac{1}{2\pi f_c}$	Delay cost of a PT1 lowpass	100 Hz → 1.59 ms
$\Delta f \approx f_\text{notch}/Q$	How surgical a notch is	300 Hz, Q=10 → ±15 Hz

Build & integration — Module 10

Formula	Answers	Reference build
$x_{CG} = \dfrac{\sum_i m_i x_i}{\sum_i m_i}$	Where the pack goes	battery over CG, always
$f_n = \dfrac{1}{2\pi}\sqrt{k/m}$	Soft-mount resonance	target 60–100 Hz
$R_\text{system} = \prod_i R_i$	Why one joint ruins a build	$0.999^{40} = 0.961$ — 1 failure per 26 flights

How to use this card

Every row is a one-minute sanity check: put your numbers in, and if the answer lands far from the reference column's ballpark, one of your inputs is wrong — usually a unit. The modules linked in each section show the full worked examples.