BLDC 32k Spin-Up + Thermal Explorer

Averaged BLDC/DC-equivalent launch model with battery sag, ESC loss, three control strategies, two identical motors, motor→plate and motor→air heat paths, plus plate convection and radiation. Everything runs locally in this single file.

Motor + mechanical

Motor Kv Kt = Ke in SI

Target speed

Motor pole pairs 14-pole 2207 = 7 pairs; used for BEMF crossing budget

Total rotating inertia motor + flywheel, reflected at shaft. 39 = flywheel alone; rotor not yet measured (fit from a launchtrace)

Motor resistance line-to-line. 24.7 mΩ measured 4-wire (2 A, 3200 KV, 2026-09-30)

Steady running current @ target per motor; flywheel aero + bearing drag. Not yet measured: read steady pack current at a 32k hold

Battery + ESC + control

Pack open-circuit voltage

Pack + wiring resistance controls voltage sag; both motors draw through it. 46 mΩ fits the run 9 sag (19.7 → ~15 V) with the calibrated drive impedance; measure it (resting vs loaded voltage) to replace this

ESC conduction resistance lumped bridge + copper. Vortex F65: two VSP003N04MS-G in the path (2.3–2.8 mΩ each) + ~1 mΩ

Drive impedance (calibrated) extra voltage-to-current impedance seen on hardware (commutation, inductance, wiring). Run 9: ~6,000 rad/s² per volt of headroom = 125 mΩ total with the 39 g·cm² flywheel, i.e. 94 mΩ on top of motor + ESC. Not counted as motor copper heat. Match the blaster's Current Cap Model Impedance (motorR + escR + this).

Post-BEMF current ceiling per motor; keep inside the ESC rating. 20 A cannot reach 32k in under ~160 ms

BEMF lock time time from the trigger to the ESC reporting RPM. Measure it: launchtrace lockMs (run 9: ~45 ms to 1,000 RPM). With the curve exported "after lock" this is spent before the curve starts

RPM at BEMF lock speed the firmware sees when it starts an after-lock curve (lock = 2 frames at or above 1,000 RPM). Read it from launchtrace startRpm

Assumed BEMF crossing count sanity check; not a stock AM32 setting

BEMF confirmation dwell consecutive lock confirmation after crossing criterion

Open-loop startup current — start independent of post-BEMF current ceiling

Open-loop startup current — at BEMF lock independent of post-BEMF current ceiling

BEMF handoff ramp blend startup current ceiling into closed-loop profile

Post-BEMF current slew limit symmetric command rise/fall limit

Speed PI catch armed at late catch zone; before this the optimized launch profile has full authority

Speed PI Kp A per 1000 RPM error; high enough to avoid a large current step-down at catch entry

Speed PI Ki A per (1000 RPM·s), anti-windup applied

Speed PI integral correction clamp

Bumpless PI tracking-bias clamp temporary handoff bias; decays to zero as RPM error closes

PI integral active band P + drag feed-forward catches first; I only trims close to target

Post-target settling simulation

Settling band around target

Continuous in-band dwell to confirm settled any excursion resets the timer

Maximum allowed overshoot

Taper starts at

Taper finish current fraction of current cap at target

BEMF qualification budget

Launch optimizer

Spin-up deadline minimize predicted burst motor temperature while meeting this time. Time to 100% of target. Exported RPM references use the simulated duration; actual blaster firing latency depends on measured wheel speed and firing gates.

Smooth freeform heat tie window prefer smoother curve only within this tiny heat difference

compare 4S / 5S / 6S full-charge voltage optimize the entire 4.2 → 3.3 V/cell discharge range optimize startup current + BEMF handoff with each strategy enforce post-BEMF current slew-rate limit layer speed PI catch / hold over every optimized strategy automatically tune PI catch settings on a small finalist set (fast staged search)

The Current cap above is the hard post-BEMF ceiling. With voltage search enabled, the optimizer compares 16.8 V (4S), 21.0 V (5S), and 25.2 V (6S), plus the exact Pack voltage slider value if it differs. It automatically varies starting current, transition RPM, finishing current, and (for 3-stage profiles) a second transition/current. Current is allowed to rise or fall — taper is not assumed. It now also tests drag-compensated constant acceleration, an adaptive deadline-tracking controller, unrestricted 8-point freeform, monotonic 8-point freeform, smooth-monotonic 8-point freeform, and a C¹ monotone cubic-spline current-vs-RPM profile. The smooth variant uses smoothness only as a tie-break when heat is within the configured tiny heat window, so it does not deliberately trade meaningful thermal efficiency for appearance. Startup current is now independent of the post-BEMF current ceiling; when startup optimization is enabled, the search also varies startup start current, current at BEMF lock, and handoff-ramp duration. The optional slew limiter is applied to post-BEMF current commands so step/freeform solutions cannot exploit instantaneous current changes. A common speed-PI catch can also cap every strategy near target RPM. The PI handoff is now truly bumpless: when the catch first arms, a temporary tracking bias is initialized so the PI output exactly matches the optimized launch current, then that bias decays to zero as RPM error closes. Integral action remains separate and small. When automatic PI tuning is enabled, the tool searches catch RPM, Kp, Ki, and integral-band settings only on the best trajectory candidates rather than multiplying the entire 10k-profile search. The simulator continues beyond first target crossing to report overshoot and settling behavior. Whole-pack mode still finds (1) one fixed profile that must meet the deadline across the discharge range and (2) a voltage-aware lookup-table strategy that can choose a different optimized profile from measured pre-launch pack voltage.

Thermal network

Number of shots

Time between shots

Ambient temperature

Effective motor thermal mass short-timescale lumped node, per motor

Motor→plate resistance per motor

Motor→air resistance per motor, spinning bell/flywheel

Plate thermal mass

Exposed plate area total area participating in convection/radiation

Plate convection coefficient

Plate emissivity 0 ≈ ignore radiation; anodized Al often high

motor→air cooling plate radiation

Model assumptions

Ideal commutation, averaged BLDC/DC-equivalent model; no field weakening, saturation, desync, or commutation timing error.
Battery sag is represented by one lumped source resistance. Under PWM, battery current is approximated as D × motor current.
Before usable BEMF is available, current follows a separate open-loop startup ramp in amperes; it is no longer tied to a percentage of the post-BEMF current ceiling. The optimizer can vary startup start current, current at BEMF lock, and BEMF handoff-ramp duration around the user-selected baseline values.
After BEMF lock, optimized profiles blend from the startup current ceiling into the selected closed-loop profile over the modeled handoff interval. When enabled, a symmetric current-command slew-rate limit is then applied to all post-BEMF controlled strategies. The absolute full-bus physical floor intentionally bypasses that post-BEMF slew limit.
Constant-current control after BEMF lock is treated as an ideal current loop. If the required duty exceeds 100%, the motor becomes voltage-limited.
The optimizer is allowed to vary current in both directions with RPM. It searches constant, ramp, 2-stage, and 3-stage profiles; a “taper” is only selected if the model actually prefers one.
When voltage search is enabled, 4S/5S/6S full-charge voltage is treated as an optimizer design choice. Pack/wiring resistance remains fixed, so this compares voltage while holding pack stiffness constant unless you change that slider yourself.
The “unoptimized” comparison is defined as the same pack voltage and same pre-BEMF startup followed by 100% duty/full-send after BEMF. This gives a clear apples-to-apples baseline for how much heat the optimized current profile saves.
The battery-degradation plots now compare three cases: the original full-charge-tuned profile held fixed, one static robust profile optimized to satisfy all sampled voltages, and a voltage-aware lookup-table strategy that selects a precomputed profile from measured pre-launch pack voltage.
The voltage-aware LUT search explicitly includes the final fixed robust whole-pack winner as a candidate at every voltage bin and re-checks that dominance at the final 0.10 ms simulation timestep. The dense 0.05 V/cell sweep may also fall back to the fixed robust profile between LUT bins. Therefore the reported dynamic LUT cannot legitimately have a shorter feasible voltage range, or higher optimized heat where the fixed robust solution is a legal choice.
The whole-pack objective hard-constrains time-to-target at seven optimizer bins from 4.20 to 3.30 V/cell and minimizes equal-bin average motor heat. Equal voltage-bin weighting is a design approximation, not a detailed LiPo state-of-charge probability model.
The displayed strategy cutoff voltage is taken from a denser 0.05 V/cell sweep. When a strategy fails below that cutoff, the model is saying that the launch misses the deadline there even with its best searched current shaping.
“Sum heat” is the simple sum of motor heat over the feasible dense-sweep sample points, included as a comparative stress metric rather than literal energy over one real battery discharge cycle.
The strategy search now also includes a drag-compensated constant-acceleration family, an adaptive deadline tracker, and an 8-point freeform current-vs-RPM family. The freeform profile is refined by deterministic coordinate descent around the best conventional result rather than brute-forcing every possible 8-dimensional combination.
The deadline tracker is a simulated feedback law: after BEMF it recomputes the average acceleration still required to reach target by a chosen finish time, adds the modeled drag-current term, and clamps the result to the current ceiling / available bus voltage.
The 8-point freeform family uses fixed RPM fractions and linearly interpolated current control points. Its purpose is to test whether the older constant/linear/staged families were artificially constraining the optimum.
Three additional 8-point families are searched: monotonic non-decreasing current, smooth-monotonic current, and a monotone cubic spline. The spline uses shape-preserving cubic Hermite interpolation, including zero slope outside the first and last knots, so its commanded current is continuous with continuous slope and cannot overshoot its neighboring control points.
The optional speed PI layer is common to every controlled strategy and acts as a late outer current ceiling near target RPM: current command = min(optimized profile, speed-PI demand, hardware ceiling). The handoff is bumpless: at first catch activation a temporary tracking bias is initialized so PI demand exactly equals the optimized profile current, then that bias decays to zero with closing positive RPM error. Integral action is a separate small correction, disabled until the error is inside the configured integral band and protected by conditional integration / anti-windup.
When automatic PI tuning is enabled, the broad ~10k trajectory search runs without PI or post-hit settling. A second-stage staged PI search is then run only on a small set of the strongest family finalists (plus the smooth-monotonic candidate). It uses a compact coarse grid followed by local coordinate refinement for catch RPM, Kp, Ki, and integral band. This keeps PI from distorting trajectory selection and removes thousands of unnecessary settling simulations.
Controlled-profile simulations continue beyond the first 32k crossing for the configured settling window. Overshoot above the configured limit makes the candidate infeasible. A controller is not considered settled until it remains continuously inside the settling band for the configured dwell time; any excursion resets the dwell timer. Full-bus physical-floor results remain a first-crossing reference and do not use PI.
PI auto-tuning now receives a trajectory timing-margin seed bank instead of only the lowest-heat trajectory sitting at the launch deadline. For a 150 ms target, finalists are deliberately retained around roughly 138, 142, 145, 147, 149, and 150 ms, plus fastest and firmware-friendly smooth/monotonic trajectories. This lets the optimizer spend a few milliseconds on the final speed catch without falsely declaring higher-voltage packs infeasible.
Across the four 8-point freeform families, the final recommendation prefers the spline, then smooth-monotonic, monotonic, and unrestricted implementations only when predicted motor peak is within 0.10 °C and heat is within the configured smooth heat-tie window. Within that thermal tie, lower pack energy is preferred before implementation smoothness. Meaningful thermal improvements always override these tie-breakers.
The optimizer's “absolute time floor” uses the same pre-BEMF startup, followed by 100% duty after BEMF. If that floor misses the deadline, no current-profile algorithm can meet the deadline without changing another physical/control assumption.
The thermal motor node is an effective short-timescale motor temperature, not a guaranteed winding hot-spot temperature.
Two identical motors are assumed. The plotted motor temperature is one representative motor; the plate receives heat from both.
Each shot deposits motor copper heat essentially instantaneously relative to the multi-second thermal time constants.

Ke = Kt

—

V/(rad/s) = N·m/A

Ideal no-load speed

—

at open-circuit pack voltage

Plate convection Rθ

—

1 / (hA), radiation separate

Motor→plate τ

—

Rcontact × Cm, per motor

BEMF acquisition

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open-loop startup phase

32k target reach times

These update directly from the spin-up solver

Full voltage

—

time to first hit target rpm

Constant current

—

time to first hit target rpm

Current cap + taper

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time to first hit target rpm

Fastest strategy right now

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based on current settings

Spin-up speed

Target line shown dashed; colored vertical markers show target-hit times

Full voltage Constant current Current cap + taper

Motor current during launch

Per motor

Temperature — burst + cooldown

Solid = motor node, dashed = plate

Launch optimizer — speed vs temperature

Not run yet

Run the optimizer after changing settings. It will test thousands of current-vs-RPM launch profiles against your deadline and thermal model, including 4S / 5S / 6S pack voltage when voltage search is enabled.

export the after-lock curve (firmware launch clock "at BEMF lock") landing from % of target slope eases to zero at the target instead of stopping dead (0 = off) Current target: ≤150 ms to 32k RPM

Recommended

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coolest profile that meets deadline

Fastest under current ceiling

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Pareto knee

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balanced speed / temperature point

Search ceiling

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maximum commanded current after BEMF

Pack voltages searched

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full-charge pack comparison

PI catch tuning

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manual / default

Control quality

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overshoot / settling

Absolute time floor

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full bus after BEMF

Deadline feasibility

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Dominant bottleneck

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BEMF startup penalty

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vs identical model with immediate BEMF

Fastest-launch time budget Run optimizer to classify the launch

pre-BEMF/open loop current-command limited 100% duty / voltage limited

Constant current Linear ramp Two-stage Three-stage ● Constant acceleration ● Deadline tracker ● 8-point freeform ● monotonic 8-point ● smooth monotonic ● C¹ monotone spline ○ 4S □ 5S △ 6S ★ recommended ● Pareto frontier

Strategy family winners — current vs RPM

best deadline-meeting member of each family at the selected pack voltage

Actual motor current; every family still obeys the same battery sag and 100% duty limit

Family	Best profile at selected voltage	Time	Motor heat	Motor peak	Peak current
Run optimizer to compare strategy families.

Optimized vs unoptimized at the same pack voltage

run optimizer to compare

Unoptimized / full-send

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100% duty after BEMF

→

Optimized

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coolest deadline-meeting profile

Motor heat saved / shot

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Motor peak reduction

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Extra spin-up time used

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Peak current reduction

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Optimized RPM overshoot

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Settling after first hit

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Current profile vs RPM

run optimizer to populate this chart

Unoptimized full-send actual current Optimized actual current ┅┅ optimized command orange wash = optimized profile voltage-limited

Speed PI catch / settling near target

run optimizer to populate PI catch behavior

solid = RPM dashed = 32k target shaded band = settling tolerance

4S vs 5S vs 6S — “wrong” vs optimized

full-bus reference compared with best deadline-meeting profile

Pack	Voltage	Full-bus time	Full-bus heat	Full-bus motor peak	Optimized time	Optimized heat	Optimized motor peak	Optimized profile
Run optimizer to compare pack voltages.

Whole-pack optimization — fixed profile vs voltage-aware control

Hard constraint: hit the deadline at every sampled voltage from 4.2 to 3.3 V/cell

Run the optimizer to calculate whole-pack robust and voltage-aware strategies.

Pack	Full-bus feasible to	Fixed robust feasible to	Dynamic LUT feasible to	Fixed robust profile	Fixed avg / sum heat	Dynamic avg / sum heat	Dynamic worst time	Interpretation
Run optimizer to populate whole-pack results.

Full-charge-tuned profile held fixed One robust profile for the whole pack Voltage-aware lookup table

Battery degradation sweeps for each optimized pack strategy

Compare full-charge tuning, one fixed whole-pack profile, and voltage-aware dynamic control

4S optimized profile vs battery depletion Run optimizer to populate this sweep.

not run deadline robustness thermal trend

Spin-up time vs cell voltage

Motor heat / shot vs cell voltage

Burst motor peak temperature vs cell voltage

Run optimizer to compare 4S battery depletion behavior.

Voltage-aware firmware lookup table choose profile from pre-launch cell voltage

V/cell	Pack V	Predicted time	Heat/shot	Profile to select
Run optimizer to populate LUT.

5S optimized profile vs battery depletion Run optimizer to populate this sweep.

not run deadline robustness thermal trend

Spin-up time vs cell voltage

Motor heat / shot vs cell voltage

Burst motor peak temperature vs cell voltage

Run optimizer to compare 5S battery depletion behavior.

Voltage-aware firmware lookup table choose profile from pre-launch cell voltage

V/cell	Pack V	Predicted time	Heat/shot	Profile to select
Run optimizer to populate LUT.

6S optimized profile vs battery depletion Run optimizer to populate this sweep.

not run deadline robustness thermal trend

Spin-up time vs cell voltage

Motor heat / shot vs cell voltage

Burst motor peak temperature vs cell voltage

Run optimizer to compare 6S battery depletion behavior.

Voltage-aware firmware lookup table choose profile from pre-launch cell voltage

V/cell	Pack V	Predicted time	Heat/shot	Profile to select
Run optimizer to populate LUT.

Start here: click “Run optimizer” above. The tool will then show an apples-to-apples comparison between the optimized launch and a full-send baseline at the same pack voltage. The vertical dashed line is your deadline. Lower-left is better. The recommended point is the lowest predicted motor peak temperature that still lands on or before the deadline.

“Motor peak” uses the current burst settings (shot count, cadence, thermal mass, motor→plate/air paths). Heat/shot is also reported so you can separate launch efficiency from thermal-model assumptions.

Strategy results

Strategy	Target	Spin-up	Motor heat / shot	Peak current	Min bus V	Pack energy / shot	Motor peak	Plate peak

Move a slider to update the model.

How to read it

The reported time-to-target starts at t = 0 and therefore includes the pre-BEMF open-loop startup interval and modeled BEMF handoff ramp. Startup current is independent of the post-BEMF ceiling. After BEMF lock, controlled strategies may also be constrained by the selected current slew-rate limit; the absolute full-bus floor remains the physical no-slew lower bound. The taper strategy intentionally gives away some acceleration near target speed in exchange for lower late-shot current and usually lower heat. Full voltage is included as an upper-performance / upper-stress reference, not as a recommendation. The thermal plot is mainly useful for comparing strategies and sensitivity to Rθ, thermal mass, airflow, and shot cadence.