I get asked this one a lot: how high can a pull-down (top-attraction) system actually float a load?
The honest answer is not a popular one — you don’t tune your way to height, you buy it. Retuning the control loop, rewinding the coil, fitting a bigger heatsink: all of that changes how stably it floats, and almost none of it changes how high. Height lives in the geometry and the materials of the magnetic circuit, and the bill is computable before you spend anything.
Here are the paths we have actually tried on PD systems, with the math and the mistakes. The numbers are relative where they should be — plug in your own specs.
First, the math nobody likes
The attraction across an air gap is F = B²A/(2μ₀). Balance it against the load and you get the required flux density, Bneed = √(2μ₀·mg/A). Stare at that formula for a second, because the interesting part is what is not in it: the gap. Given a payload and a pole area, the B you need is fixed. The gap does not get a vote.
What the gap does tax is ampere-turns: NI = B·h/μ₀, doubled if your circuit runs two gaps in series. Copper loss follows ampere-turns squared. Put the two together and you get the law that runs this whole business: P ∝ h². Double the gap, quadruple the power.
| Gap h (mm) | 15 | 20 | 25 | 30 | 40 | 50 |
|---|---|---|---|---|---|---|
| Relative power | 1.0 | 1.8 | 2.8 | 4.0 | 7.1 | 11.1 |
| What that means on the bench | Natural cooling | Fine | Start thinking about heat | Heatsink + airflow | Thermal design is now a main cost | Consumer grade, forget it |
This is why so many large-gap PD products run like space heaters. It is not that their makers skipped thermal design — the architecture makes you buy every extra millimeter with sustained current.
Path 1: let the magnet carry the weight
If Bneed is a constant, the obvious question is how much of it really has to come from the coil. Turns out: not much. Put a permanent-magnet ring in the circuit and let the coil cover only the shortfall. We call the magnet’s share the bias ratio, η = Bpm/Bneed. The coil supplies (1−η) of the ampere-turns, and since power goes with the square of ampere-turns, the payoff is quadratic: P/P₀ = (1−η)².
| Bias ratio η | 0 | 50% | 80% | 90% | 95% | 99% |
|---|---|---|---|---|---|---|
| Coil still has to supply | 100% | 50% | 20% | 10% | 5% | 1% |
| Relative power | 100% | 25% | 4% | 1% | 0.25% | 0.01% |
Going from 80% to 95% moves only fifteen points of load onto the magnet and cuts the coil power sixteen-fold. Nothing else in the design comes close to that lever.
A real case. A 50 kg display piece at a 40 mm gap on an Ø100 iron-core pole face: the balance works out to Bneed ≈ 0.40 T, and pushing that across two 40 mm gaps needs about 25,000 ampere-turns. With 2,000 turns and roughly 8 Ω of winding:
| Scheme | Coil current | Copper loss |
|---|---|---|
| Pure electromagnet (η = 0) | 12.6 A | ≈ 1.2 kW — call it 2–3 kW with driver losses |
| 95% bias | 0.63 A | ≈ 3 W |
I will admit that the first time I ran these numbers I went back and checked the arithmetic. Two orders of magnitude, from one design decision.
One thing has to be said plainly, because the market is full of hand-waving on this point. The vertical axis of a PD system is positive feedback — closer means stronger pull means closer — so the control loop must stay powered at all times. Bias can press the static power extremely low, but never to true zero. Anyone selling a “zero-power PD” is bluffing.
There is also a side benefit worth having. Expand the force around a biased operating point and the cross term (Bpm·ΔB·A/μ₀) dominates: the controllable force becomes essentially linear in current, with the gain amplified by Bpm. A pure electromagnet is square-law and single-polarity; a biased one behaves. Loop tuning gets much easier, and the bigger the gap, the more you appreciate it.
Path 2: close the magnetic circuit
The crudest-looking step was the most effective one in our tests: bolt an iron plate on top of the core. The flux gets a low-reluctance return path, total reluctance drops, and the same ampere-turns push more flux across the gap. Since force goes with Φ², doubling the flux quadruples the force.
The part that matters for height is the decay exponent. In a closed circuit, force falls off roughly as 1/h². In an open circuit — think push-up repulsion — it is closer to 1/h⁴. So the same plate and the same doubling of circuit efficiency buys about +41% height on a PD system and only +19% on a push-up one. This is a PD trick; on PU it underwhelms.
Sizing the plate is one inequality: Afe ≥ Φ/Bdesign, with Bdesign around 1.0–1.3 T so the iron stays clear of saturation. Two things we learned the slow way. One, the plate’s outer diameter must be larger than the magnet ring’s — a small plate cannot catch the flux and you might as well not fit it. Two, do not go thin: a saturating plate is worse than no plate, because you get the parasitic pull and the weight without the gain.
The cheapest way to find the thickness knee is not simulation. Tape on 1 mm plates one at a time, measure the gap each time, and stop when the curve bends. The stack of plates beats the simulator at this stage, every time.
Path 3: a small magnet on top, for the last few millimeters
With the bias and the plate in place, a small permanent magnet above the plate squeezes out a bit more. A full ring or four small pieces spaced around the circle — we tested both and honestly cannot tell them apart. The far field only cares about total moment, and the discreteness shows up only in higher-order terms, which decay one order faster and are gone by the time they reach the floater.
The gain is modest and computable: h₁/h₀ = (1+η′)1/4, where η′ is the top magnet’s field share relative to the coil’s.
| η′ | 20% | 35% | 50% |
|---|---|---|---|
| h₁/h₀ | 1.047 | 1.078 | 1.107 |
| Gain from a 25 mm baseline | +1.2 mm | +1.9 mm | +2.7 mm |
Do not get greedy with this magnet. There are two ways it ends badly: static pull exceeding mg locks the floater against the core and your gap goes to zero; and every point of share the magnet eats is dynamic margin the coil loses, until one disturbance is enough to lose the float. We hold the total bias at 80–95% and leave the rest to the coil. That split came out of testing, not out of caution.
One more note if you use four discrete magnets instead of a ring: the flux concentrates at four landing spots, and the plate can saturate locally there first. A matrix layout needs more thickness margin than a ring layout.
Path 4: high voltage and a switching stage
No height in this one directly, but without it the first three paths don’t land. A 3 kW load at 220 V is 13.6 A; at 12 V it is 250 A — that is not a power supply, that is a welder. Large-gap PD ends up on rectified mains, around a 310 V bus. Same story in the drive stage: at high current a linear pass device is a stove, so you switch and take the Rds(on) and edge losses instead.
And one underrated reason to raise the bus: di/dt = V/L. A bigger gap demands faster correction — the same position error must be caught in less time — and only voltage buys current ramp rate. Bandwidth follows the bus.
Path 5: the one everyone skips — 4-axis balance
Add the bias ring and the floater stops sitting politely on the axis. It drifts toward one side of the ring and sticks there. We hit this on the bench; it is not a theoretical worry. Large-gap PD needs at least four balance axes — two directions, two independent channel pairs. Leave one pair out and the symptom is always the same: “it pulls to one side.”
An honest caveat: the lateral axes are an order of magnitude weaker than the vertical pull, by physics. Mechanical coaxiality comes first; the electronics are the net, not the rope. If the structure is assembled crooked, no amount of channels will save it.
Power loss: decide on day one
The question nobody wants to ask: when the power dies, what happens to the floater? A broken exhibit is the small case. Hitting someone is the real one.
Here is the counter-intuitive part. At the instant of power loss only the permanent magnet remains, and force goes with the square of the field: Fhold = η²·mg. At 95% bias that is 0.90·mg — the floater still falls. Even an aggressive bias does not survive a blackout.
What does work is running the bias slightly hot: size the magnet for 1.15× the requirement and let the coil cancel the excess during normal operation. When power dies, the canceling current vanishes with it, the pull jumps to 1.15² = 1.32·mg, and the floater snaps up against the core instead of dropping. The price is a few watts of static power in normal running — against zero falls for a tens-of-kilograms exhibit, not a hard call.
Design the release in advance, though. Once snapped up, the near-field pull is 5–10× the weight — nobody is pulling that off by hand. A threaded jack, a lever, a wedge: some mechanical separator is a deliverable, not an accessory.
If I had to rank them
| Measure | What it buys | What it costs |
|---|---|---|
| ★★★★★ PM bias | Power falls with (1−η)² — the only lever that moves orders of magnitude | Magnet cost |
| ★★★★★ Back iron | +41% height on PD (closed circuit) | Plate cost, some parasitic pull — size it generously |
| ★★★★ HV + switching drive | Makes the first two land | Safety compliance, device ratings |
| ★★★ Top bias magnet | The last 1–3 mm | Cheap — but oversize it and it locks on |
| ★★★ 4-axis balance | Kills the side-pull failure mode | Channel count doubles; coaxiality still comes first |
| ★★ Bigger pole area | Load and height together | Volume and cost, linearly — crude but reliable |
| ★ Higher magnet grade | Same volume, higher working point | Material cost and thermal headroom — geometry unchanged |
Field notes
- Don’t chase the bias past 95%. The savings above it don’t pay for the stability margin they eat.
- Find plate thickness with the stacked-plate scan, not the simulator.
- Test the top magnet reversed first. Reversed should measure worse — if it measures better, your original orientation was wrong.
- Run the power-cut test ten times, not once, and at different gaps and temperatures.
- Never trust a simulated absolute height. Assembly gaps, magnet consistency, thermal drift — simulation shows trends, the bench gives numbers.
None of this is exotic. It is a handful of explicit choices, each with a price tag you can compute in advance — which is the whole point.
Engineering notes from our bench. The formulas and the worked example are for design reference — not product specifications or delivery commitments.
If you are weighing architectures, the companion pieces are where PD is going next and why our push-up systems need no positioning aid. A working large-gap PD build: the 42 cm globe we did for a school. And if you have a load and a target gap in mind, send them over — I would rather compute the bill before you spend anything.