Shaft power W · inner left
Torque N·m · inner right
Current iqmax A pk · outer right
Efficiency η % · outer left
Motor
Preset
Name
Motor Kv
rpm/V · mech speed per volt
Pole count
magnets · even · pp = poles/2
Phase inductance L
µH · per convention below
Phase resistance Rs
mΩ · per convention below
R & L entered as
meter across 2 wires = ph–ph
What this computes · R & L entry conventions
Computes, for every speed to base speed, the maximum q-axis current the
inverter can still regulate — where back-EMF + resistive drop +
inductive drop fills the voltage circle. All equations use
phase-neutral R and L; an LCR meter across two motor wires reads
phase-to-phase (2× larger). Set the entry convention here
— the converted values actually used are echoed under the
headline numbers.
No-Load Drag
Unloaded current I0
A pk · iq spinning unloaded · blank = off
…measured at
RPM · speed of that measurement
How drag is modelled
Optional iron + windage + friction model. Drag torque is taken
proportional to speed through your measurement (drag current
id = I0·rpm/rpm0), subtracted
from every torque and power point and charged against efficiency.
Limits & Losses
Max current rating
A pk · thermal / ESC · blank = off
Copper loss factor
× I²R · skin + hot windings · 1 = DC 25 °C
Stray load loss
% of shaft power · 1–3 typ · 0 = off
Cap · loss factors — how they're applied
Current cap — optional. Clips every curve at this current;
the peak-power point is recomputed with the clip applied and the cap is
drawn on the charts.
Loss factors — loss accounting only; the torque/current
curves do not move. The copper factor multiplies I²R for winding
temperature (copper is +0.39 %/°C, so ≈1.37× at
120 °C) and AC skin/proximity effect at high electrical
frequency — 1.4–1.6 is typical for a hot motor at speed.
Stray load loss is the IEEE 112-style allowance for
load-dependent iron, magnet eddy and PWM ripple losses that no-load
drag can't see — 1–3 % of shaft power is typical.
Together with a measured no-load drag these bring the efficiency
figure in line with dyno-measured datasheet maps.
Drive
Bus voltage Vbus
V DC · assumed stiff
Modulation
sets vlim: Vbus/√3 or /2
Timing advance
° elec · trapezoidal only · 0–30
Demag angle limit
° elec · 20–23 typ · 0 = off
Voltage margin
0.85–0.95 practical · 1.00 ceiling
Trapezoidal mode · timing advance · demag limit
Trapezoidal = classic 120° six-step block commutation, modelled by
its voltage fundamental: ceiling ≈ 0.605·Vbus
(π/3 above SVM, so base speed ≈ 1.047·Kv·Vbus),
block-harmonic copper factor π²/9, and R appearing π/3 stronger
in the voltage limit. Timing advance fires commutation early so the
current leads the back-EMF — field weakening that trades torque
for speed; the curves extend beyond base speed accordingly. The demag
limit is the sensorless constraint: after each commutation the outgoing
phase must freewheel to zero (decay rate (Vbus+2·EMF)/3L)
before the next zero crossing or sensing is lost — it caps current
ever harder as RPM rises and usually binds before the voltage circle at
speed. Enter the tolerable angle at zero advance; advancing commutation
moves it away from the zero crossing, so the usable window is the set
angle plus the advance — which is why more timing lets a
sensorless drive carry more current.
Base Speed
—
iq → 0 · unloaded top speed
Peak Shaft Power
—
—
Peak Efficiency
—
best point of the modelled η curve
model uses
L ph–n —
Rs ph–n —
ψ —
vlim —
Effective Kv rpm/V · left
Net torque N·m · right
x = load current · dashed = no-load Kv
Height + colour: η · red low → blue best
Load axis clipped at iqmax(rpm)
hover for values · drag to rotate
Operating Point
Speed
RPM · blank = off
Current
A pk fundamental · blank = max at speed
Current iq
peak phase · iqmax when blank
RMS phase current
true RMS · incl. block harmonics
Torque
1.5·pp·ψ·(iq − idrag) · net
Shaft power
T · ωm
DC bus draw
(P + losses) / Vbus · approx
Losses · Voltage Budget
Copper loss
1.5·kcu·Rs·iq²
Drag loss
iron + windage · from I0 · 0 = off
Stray loss
load-dependent iron · % of shaft · 0 = off
Efficiency η
P / (P + Pcu + Pdrag + Pstray)
Back-EMF
ωe·ψ · V pk ph–n
Resistive drop
Rs·iq · V pk ph–n
Inductive drop
ωe·L·iq · V pk ph–n
Vector total vs vlim
√(Vd²+Vq²) · flags unreachable points
Reading the efficiency surface
Every operating point the drive can reach: speed along one axis, load current
along the other, efficiency as height and colour. The clipped far edge of the
surface is the voltage-circle limit iqmax(rpm) — the same curve
as the Curves tab. The current cap and no-load drag are applied when set. The
load axis tops out just above the peak-power current (or at the cap) —
higher currents are reachable only near stall and would crush the useful region.
Assumptions & model limits
Steady-state only, with id = 0 — no field weakening, so a drive
with FW can exceed base speed and these curves. L and Rs are taken
constant: no magnetic saturation (saturating L shifts high-current numbers) and
no temperature rise (hot Rs shifts low-speed numbers). No switching
losses; iron, windage and friction are modelled only if a no-load measurement
is entered — drag torque is then taken proportional to speed through that
point, which is a one-point fit: it understates constant friction at low speed
and any ω² windage growth at high speed. Without it, copper is the
only loss modelled. The bus is assumed stiff; sag under load
lowers vlim and every curve with it. The margin input exists because
real current controllers need voltage headroom to regulate — running at
100 % utilisation is exactly how drives lose regulation and desync.
Trapezoidal mode is a fundamental-equivalent model of 120° six-step
(±5 % versus exact waveform simulation); timing advance is modelled
as the current fundamental leading the back-EMF by the advance angle, and all
displayed currents remain fundamental amplitudes (block flat-top ≈
iq/1.103, RMS shown includes the block harmonics). The
stall figure is the resistance-limited current vlim/Rs
— the point where the entire inverter voltage ceiling is dropped across
the winding resistance (line-to-line: √3·Rphn·iq
= Vbus) — and real motors reach thermal limits far below it.