Teach the physics. Grade the numbers.
A rotorcraft performance engine your students can see all the way through: momentum theory, a real power-required curve, a wing model with a stall boundary, every governing equation written out and re-derived in the browser, then tested against a real aircraft on the bench.
Start with the public math: rotorlab.app/how-we-validate needs no account.
A semester of aeronautical engineering, on one tool
Each unit is a topic your syllabus already carries, taught with the equation in one hand and a live aircraft model in the other.
1 · Aerodynamic foundations
Momentum theory, disc loading and the atmosphere. Why a larger prop hovers cheaper and why a hot day at altitude punishes every rotorcraft, with both effects moving the numbers as the equation says they must.
2 · The powertrain as a system
Packs, parallel packs, named buses and regulated BEC rails, every rail checked against its regulator and every pack against its C-rating.
3 · Whole-aircraft performance
The power-required curve across airspeed. Best-endurance speed is the minimum of a curve the student built; top speed comes out thrust-limited or power-limited, and the tool says which.
4 · Winged and VTOL flight
A wing with area, aspect ratio and span efficiency, a stall speed the aircraft must exceed, and a transition-feasibility check: can the thrust-borne phase accelerate past stall at all?
5 · Measurement against theory
The calibration lab. Predict hover current from the model, hover the real aircraft, and invert the measurement into a figure of merit. The gap is the lesson.
6 · Design-space exploration
Trade studies sweep one variable and re-analyze everything at each point. The endurance-versus-capacity curve flattens because the bigger pack weighs more, and students see it before the instructor says it.
Predict. Fly. Measure. Reconcile.
The lab exercise the whole tool is built around, runnable with one aircraft, one battery and one bench.
Predict
Students model the lab aircraft in the Builder and commit to numbers: hover current, hover throttle, endurance. On paper, in advance, from theory.
Fly
Hover the real aircraft. Live Telemetry reads the flight controller in the browser over USB, the LAN or the cloud relay: nothing to install on lab machines.
Measure
Live Calibration averages the steady hover and inverts it: the measured figure of merit falls out of the same equations the students derived, and max thrust is inferred from the hover, or measured with a thrust-stand file.
Reconcile
Predicted versus measured, side by side, with percentage deltas. Why is the rotor's figure of merit 0.55 and not the 0.65 the model assumed? That discussion is the course.
The derivation stays on the whiteboard
The first problem set is the same one it has always been. What changes is everything after it: the configuration is described once, and every dependent figure recomputes on every keystroke.
- One configuration, every consequence. Change the pack and the endurance, sag, rail headroom and thrust margin all answer at once.
- A 21-point sweep in a keystroke. The trade study re-analyzes the entire aircraft at every point, pack-mass feedback included.
- Hundreds of iterations a semester, not three. When iteration is free, students explore the design space instead of defending the first configuration that survived their arithmetic.
- The error surface shrinks to the ideas. No transcription slips, no unit mix-ups between worksheets.
One organization account is the classroom
Roster, groups, a shared library and a kept lab notebook, with nothing to install.
Roster and groups
Invite the class, organize sections into groups, reset a forgotten password in one click, and read the activity log when something needs explaining.
Shared team library
Students keep private build libraries and publish chosen builds to the organization, where the whole class can open, compare and critique them.
A lab notebook, kept
Every saved revision is dated and keeps the note typed with it. Build history lists the revisions and compares the inputs each one changed.
Submittable deliverables
One click exports a self-contained HTML report of any build: the assumptions, the figures, the charts. It opens anywhere.
Free on-ramps
The Log Analyzer reads any ArduPilot, MAVLink or PX4 flight log free, and the math page is public. Students can start the week before the department buys anything.
Nothing to install
Every tool runs in the browser, on the machines the lab already has. Live telemetry reaches a flight controller over USB from the browser itself.
The specifics
The governing relations the engine computes, exactly as the Math and Validation page writes them out, and how a department buys.
The equations in use eight relations
Hover: actuator-disc momentum theory
Induced power per disc from the thrust it carries, air density and disc area, summed across rotors and divided by the figure of merit (default 0.65) for real power. Coaxial layouts stack two motors on one disc location and carry the measured power penalty: ×0.943 against one disc carrying the pair, about 1.33 times the power of two rotors flying apart. A saved build keeps the value it was saved with.
The atmosphere: ISA density altitude
Air density from the standard-atmosphere model at the entered altitude, then corrected to the real temperature. Hot-and-high is the worst case for any rotorcraft, and the endurance and thrust penalty appears directly in the readout.
Forward flight: the power-required curve
Induced power falls with speed, profile power holds roughly constant, and parasite power rises as the cube of speed through the flat-plate drag area f. Best-endurance speed is the curve's minimum; best-range speed maximizes distance per unit energy; top speed is limited by the smaller of available thrust and available power.
The VTOL wing model
The wing is the airfoil arms: area from arm count, length and chord. Induced drag comes from aspect ratio and span efficiency. The tool reports stall speed, wing loading, cruise speeds and range, and whether the thrust-borne phase can accelerate past stall at all.
Static thrust: an estimate that says so
With no measured thrust, the engine estimates from a pitch- and blade-aware static thrust coefficient and flags every dependent figure [est]. Enter a thrust-stand value and the flags clear. Students learn to read the difference between an estimate and a measurement, because the software refuses to blur it.
Radio links: the link budget
Free-space path loss (Friis), the line-of-sight horizon from both antenna heights, first Fresnel-zone clearance, and the two-ray ground-reflection model. An aircraft must close every link it carries, and its usable range is the shortest of them.
Mass properties and balance
Every component placed on the airframe moves the CG by its mass moment. On winged aircraft the CG reads as a percentage of mean chord, the standard aviation measure. Mass is conserved by construction: the placed items sum exactly to the all-up weight the analyzer reports.
Calibration: inverting the model
A steady hover fixes the real figure of merit from measured voltage and current. A bench wide-open-throttle burst adds an inferred max thrust from the power ratio, because induced power scales as thrust to the 3/2; it assumes a static burst at 95% throttle or more, the same rotor figure of merit at both points and the motor and ESC losses the build describes, and the result lists those assumptions. Only a thrust-stand file is a measured max thrust.
What the model does not capture
The model states its own limits on the page, because teaching what a model does not capture is part of the engineering:
- It is a first-order model: strong for sizing and planning, not a substitute for flight test.
- The forward-flight curve uses a constant profile-power term and a single flat-plate drag area, not a full blade-element model.
- Static thrust estimation is coarse by design; a measured thrust-stand value is always preferred, and unmeasured figures stay flagged [est].
- Radio range excludes terrain, interference and multipath; measured range remains definitive.
How a department buys
Each published plan has a user limit, and every account in the organization counts toward it, a pending invitation and a former student's account included, for as long as the account exists. Tell us how many students and staff will sign in each term when you request program pricing, so the plan you start on fits the whole year.
Buying through your school's purchasing office: choose Pay by purchase order at checkout where it is offered. Access opens when RotorLab approves the order, and the invoice is issued then with its number, service period, due date and your purchase order number. A plan on a purchase order is invoiced again before each period ends until you cancel, and an invoice adds no tax when your billing details carry a tax exemption certificate. Annual prices, where a plan has one, are on the pricing page.
Your graduates carry the workflow with them: students who learn performance analysis here graduate into UAS programs, public-safety flight operations and design teams already fluent in the tool those operations run on.
What this page needs: the Builder, the math page and design sweeps come with every plan. The calibration lab reads the aircraft live, which needs the Live Telemetry add-on; Studio includes it, and it is on during the 14-day trial.
Teach the derivation, then teach the judgment.
On the class of tool the job actually uses. Tell us how many students and staff sign in each term.
