Port-to-Throat Ratio
The port-to-throat ratio is the cross-sectional area of the grain's core (the port) divided by the area of the nozzle throat. It is one of the first numbers to check on a new solid rocket motor design, because it tells you whether the nozzle is really the narrowest point the exhaust has to pass through - or whether the core of the grain is close to taking that job over.
port-to-throat ratio = port area / throat area
For a simple round core and a round throat this is just the square of the diameter ratio: a 1.0 in core over a 0.5 in throat is (1.0 / 0.5)² = 4.0. A ratio of 2 corresponds to a core about 1.41 times the throat diameter.
Some design guides and spreadsheets quote the same thing the other way up, as the throat-to-port ratio (throat area / port area). That is simply the reciprocal: a port-to-throat of 2.0 is a throat-to-port of 0.5. BurnSim shows both, so you do not have to convert.
Why it matters
All of the gas generated in the motor has to flow out through the core of the aft-most grain before it reaches the nozzle. If that core is not comfortably larger than the throat, the gas is moving fast along the propellant surface - in the extreme, approaching the speed of sound in the core instead of in the nozzle. Fast-moving gas scours the burning surface and raises the burn rate, which is erosive burning. The result is a pressure spike early in the burn, before the core has opened up, and on a marginal motor case that spike is what causes a CATO.
The usual rule of thumb for hobby motors is a port-to-throat ratio of at least 2 at ignition. Plenty of real motors fly below that on purpose - a lower ratio packs in more propellant for the same case - but below 2 the margin is something the designer should understand and justify, ideally with erosive burning modeled rather than ignored.
Because the core burns outward, the ratio rises through the burn. The number that matters is the one at ignition, when the core is smallest.
The ratio is closely related to two other figures BurnSim reports: Kn (burning surface area over throat area), and peak mass flux, which is the more direct measure of how hard the gas is flowing through a port. Port-to-throat is the quick geometric check; mass flux is the physical quantity behind it.
Where it appears in BurnSim
- Results Tab - the Port/throat line shows the ratio at ignition for the aft-most grain, with the throat/port reciprocal beside it, for example
Port/throat: 2.83 (throat/port 0.353). It is coloured and labelled by how much margin there is:- above 2.0 - no highlight.
- 1.25 to 2.0 - highlighted yellow, marginal (2.0 is the usual minimum).
- below 1.25 - highlighted red, LOW - erosive burning risk.
- An end burner has no core, so it shows n/a (no core).
- Design warnings - when you run a simulation, BurnSim adds a warning above the results if the throat is getting close to the aft grain's port (ratio 1.5 or below), a stronger one when erosive burning and burn-rate spikes are probable (1.25 or below), and a third when the core is actually narrower than the throat (1.0 or below).
- When the core is narrower than the throat, BurnSim uses the core as the motor's effective throat in the Kn and chamber-pressure calculation, until the burn opens the core past the nozzle throat diameter. This is the real physics - the narrowest point limits the flow - and the warning tells you it is happening.
- Erosive Burning - with erosive burning turned on, BurnSim models the burn-rate increase that a tight port causes, rather than just warning about it. This is the way to find out how much a low ratio actually costs your motor.
- Motor Report - the printed / PDF report lists Port/throat area ratio with the throat/port reciprocal, alongside the other headline numbers.
- The ratio is measured against the aft-most grain in the stack (the one next to the nozzle), because every grain's gas has to leave through its port. For non-circular cores - Fin-o-cyl, Star, C-Slot and the rest - and for tapered cores, BurnSim uses the real port area of that shape at the nozzle end, not a diameter.
Raising a low ratio
- Open up the core of the aft grain, or of every grain (at the cost of some propellant).
- Use a smaller throat - which also raises Kn and pressure, so recheck both.
- Open the core on the aft grain only, where the mass flow is highest, and keep the forward grains tighter. A Tapered Core, whose core is widest at its aft mouth, puts the extra port area in the same place.
- Model it: turn on erosive burning and see whether the early pressure peak is actually a problem for your case, rather than designing to the rule of thumb alone.