John S. DeMar
Go here for some example thrust curves and photos.
Go here for simulation examples.
The practical aspects of erosive burning are: how to predict it, how to design around it, and how to test for it. The concepts and basic theory regarding mass flux and erosive burning are covered elsewhere, so let's talk about some practical tools and tricks.
How to predict erosive burning:
First, it is a general rule that long motors will be erosive. With a standard bates grain geometry, a large burning surface area means there will be a lot more combustion gases flowing, especially at the bottom grain. A general rule is if you have length/diameter of >=8 (measuring the propellant itself, not hardware) you should be concerned. With nominal bates grain geometries, this is a 5-grain motor.
Second, it depends on the propellant. There's quite a bit of research described in the professional literature on this topic. The results aren't all that intuitive. If the propellant has a rough surface (larger AP size) it is more erosive. If the propellant is opaque, having less heat transfer into its surface, it is less erosive. If the propellant has high metals (more heat transfer) it is more erosive. A poorly-bonded high-solids mix is also more erosive.
Erosive burning will also increase under acceleration. Be a little more conservative with test stand data if you plan on a high-g flight.
Another point often mentioned is that higher burn-rate propellants are *less* erosive. This is usually due to the smaller particle sizes in fast propellants, giving smoother flow at the burn surfaces.
And finally, get Burnsim or Tamex and understand what it's telling you. Burnsim plots the mass flux, but doesn’t include it in the simulation. Tamex uses a threshold to begin applying a higher burn-rate exponent, which shows on the thrust curve itself. Keep the mass flux under 2 lbs/sqin/sec for well-behaved propellants. For stuff with lots of 400u AP, high metals, and/or questionable binder adhesion, stay closer to a mass flux of one.
How to design around erosive burning:
With a long motor, the nozzle grain will see the most "stuff" passing by at the highest velocity. To reduce the traffic jam, make the road wider. Open up the core diameter of the bottom grain, and re-simulate. You can estimate what's happening at the next grain (up from nozzle) by multiplying by the ratio of remaining grains (mass flux times 5/6 for example). Keep stepping the core diameter (less as you go up) to reduce the mass flux below your desired maximum value.
You can also make longer grains, with fewer bates grains in the same motor length. This reduces the surface area at the beginning of the burn (fewer end-faces), but increases the surface area mid way (progressive burn). In some cases, the aft core doesn't need increasing.
For a propellant with a lot of sparky stuff, the erosive affect will start sooner - at lower mass flux in a motor that's not very long. Be more conservative until you have some test-stand data.
How to test for erosive burning:
The thrust curve will have a characteristic 'erosive spike' at the beginning. This is not a short kick from the igniter, but a little longer 'bump' in the curve. If this peak is too high, the casing may be damaged, or the nozzle may blow.
I've found that it's best to start with low mass flux (larger aft core diameter), and re-test with a little smaller of a core at the nozzle grain. You should see a slight bump at the beginning of the curve when the mass flux is getting too high. You can use this threshold in Tamex.
If you like living on the edge, design your motor to take the increased pressure and use the shape of the curve as a desired feature. This would give added thrust to get a rocket off the pad. If it doesn't disassemble itself first!