Results Tab

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The Results tab is the first of the three tabs in the bottom-right panel of the BurnSim 4 main window; the other two are Test Data and Notes (see Results, Test Data and Notes). It is a plain-text summary of the burn, rewritten from scratch every time the simulation runs.

This page describes every line the tab can print. For a walk-through of a first motor rather than a field-by-field reference, start with Getting Started with a Basic Simulation.

A complete example

This is the whole panel for the demo motor pictured on the Main Page - three 2 in finocyl grains, 4 in long, 0.6 in cores, ends uninhibited, Viper propellant, through a 0.5 in throat and 1 in exit: 

Note: simulation ended at 1% of max thrust - burn time and total impulse exclude the tail past that point.

Designation:     K-1116  (32% K)
Total impulse:   1685.2 N-sec
Burn time:       1.51 s
Peak pressure:   1407 psi
Peak thrust:     407.0 lbf
Avg thrust:      250.9 lbf
Delivered Isp:   210 s
Kn max:          420.0
Kn min:          61.0
Kn avg:          302.0
Erosive burning: off
Web thickness:   0.40 in
Port/throat:     2.83   (throat/port 0.353)
Propellant mass: 1.805 lb
Propellant length: 12.00 in
Initial free volume: 7.59 in^3
CuO/Al igniter:  1.93 g  (by burning surface)
Free-vol igniter: 0.50 g  (by free volume)
Peak mass flux:  3.169 lb/in^2-sec (grain 3)
Peak mass flow:  1.889 lb/sec

The panel scrolls; on a short window the last few lines are below the fold, which is worth knowing before concluding a figure is missing.

Messages

Anything BurnSim wants to say about the design is printed above the numbers, not below them, so it cannot be missed by not scrolling. Each message carries its severity in brackets:

  • [Critical] - the simulation could not run, or ran meaninglessly. A missing throat diameter, a propellant with no C*, a grain whose dimensions are impossible (core wider than the grain, for instance), or a grain type that needs the graphical eroder while the analytic surface-area method is selected. Fix these before reading anything below them.
  • [Warning] - the run completed, but something about it deserves attention. The commonest is a core narrower than the nozzle throat, where BurnSim substitutes the port area for the throat area in its Kn calculation and says so (see port/throat ratio below). Others cover a very low Other Cf losses setting and a burn that hit the maximum simulated time.
  • [Info] - housekeeping rather than a design problem, most often about propellants: a motor file naming a propellant that was not in your database (so it was added), or one whose stored values differed from the file's.

Two further notes appear without a severity tag, because they describe the run rather than fault it:

  • A nozzle efficiency warning when Other Cf losses is below 75%. That field scales every thrust figure below it, and a value that low is usually a typo, or a leftover from before the divergence half-angle took over divergence loss.
  • A truncation note when the End sim at __% of max thrust cutoff stopped the run early, as in the example above. It matters because burn time and total impulse then exclude the tail, and nothing else in the panel would reveal that the motor did not burn to completion.

The summary lines

Line What it is
Designation The standard motor designation - class letter, then average thrust in newtons, so K-1116 is a K motor averaging 1116 N. The parenthetical is how far into that class the total impulse falls: 32% K means 32% of the way up the K band (1280-2560 N-sec), so this is a low K. 0% is the bottom of the class and 100% the top.
Total impulse Thrust integrated over the burn. This line has its own unit override in the Units menu, on by default, that locks it to N-sec regardless of the Imperial/Metric setting - the class designation above it is defined in newton-seconds, and the two disagreeing would make the designation unreadable. Turn the override off and it follows the global setting like everything else.
Burn time Time from ignition to the end of the run. Shortened by the thrust cutoff when that is on.
Peak pressure The highest chamber pressure at any point in the burn. The single most useful number for casing and closure design.
Peak thrust The highest instantaneous thrust in the burn.
Avg thrust Total impulse divided by burn time. Sits directly under peak thrust because the pair is the point: how peaky the motor is. Note it follows the Imperial/Metric setting even when total impulse is locked to newton-seconds, so on an Imperial display the two are in different units by design.
Delivered Isp Specific impulse actually delivered - total impulse divided by propellant mass. Unitless in the sense that matters: it comes out in seconds either way, so the Imperial/Metric setting does not affect it. Omitted entirely when the motor has no propellant, rather than printed as zero.
Kn max / min / avg The Kn (burning surface area divided by throat area) at its highest, lowest and mean over the run. Max and min alone say how far Kn swung but not where it spent the burn - a motor that spikes for two time steps and one that runs high throughout can report the same maximum - so the average is given alongside them. All three are ratios of areas and carry no units.
Erosive burning Whether axial slicing is on, and if so whether it actually did anything: either off, or on, peak burn rate augmentation +x%, or on, no augmentation triggered this run. Turning the feature on does not imply the crossflow ever got restrictive enough to augment the burn rate, and this line answers that directly instead of leaving it to be inferred from a kink in the pressure curve. See Erosive Burning.
Divergence loss Only when a divergence half-angle is set. The percentage of momentum thrust the cone's divergence costs, with the half-angle it came from. Motors saved before that field existed do not get this line at all, rather than a line reading "none" on every one of them. See nozzle cone geometry.
Ambient Only when "Climbs during the burn" is on. The ambient pressure range the run covered and the elevations it interpolated between, linear in elevation over the burn.
Web thickness The web of the thickest grain in the motor - the distance the burn front has to travel to consume it. Not a sum over the grains: the thickest one is what sets when the motor burns out.
Port/throat Port area over throat area at ignition, with the reciprocal alongside. See below.
Propellant mass Total propellant loaded, summed over every grain from its volume and its propellant's density. A grain with no propellant assigned contributes nothing.
Propellant length The grain lengths added together. This is propellant only - it says nothing about the casing, and does not include inter-grain spacing or head-end space.
Initial free volume The gas space in the motor at ignition. See below.
CuO/Al igniter and Free-vol igniter Two published estimates of the igniter charge this motor wants. See below.
Peak mass flux The highest mass flux seen anywhere in the motor at any time, with the grain it occurred in. Mass flux is computed at the aft end of each grain in turn as the gas generated by that grain and every grain ahead of it divided by that grain's port area - which is why it normally peaks in the last grain, the one all the exhaust has to pass through. High mass flux is what drives erosive burning; an end burner has no port and reports zero.
Peak mass flow The highest total gas generation rate of the whole motor - burning surface times burn rate times density. Unlike mass flux this is not per-grain and has nothing to do with port geometry; it is what the nozzle has to pass.

Units

Most lines follow the Imperial/Metric setting in the Settings menu. Four deliberately do not:

  • Total impulse is locked to newton-seconds by default, for the reason given in the table above - a Units menu item turns the lock off.
  • Delivered Isp is in seconds in both systems, because the units cancel.
  • Kn and port/throat are ratios of areas, so they are unitless.
  • Both igniter masses are always in grams. This is a quantity you weigh out on a scale, and even a 50 kg motor only wants a few tens of grams - pounds would round almost every realistic charge to 0.00.

Mass flux and mass flow do carry a unit suffix here. The corresponding traces on the graph do not.

Port/throat ratio

The Port/throat line states the area of the aft grain's port divided by the area of the nozzle throat, with the reciprocal (throat/port) alongside it, since both conventions are in common use: 

Port/throat:     2.83   (throat/port 0.353)

It is measured at ignition, against the last grain in the motor - the one every grain's exhaust has to pass through on its way out, and so the one that restricts first. Both numbers are ratios of areas, not diameters, and are unitless, so the Imperial/Metric setting does not affect them.

Rules of thumb: a ratio of 2 or more is the usual design target; below about 1.25 the port is restrictive enough that erosive burning and a burn rate spike become likely; at or below 1 the port is narrower than the throat, and BurnSim substitutes the port for the throat as the effective area in its Kn calculation - which it warns about at the top of the tab. An end burner has no port, so it reports n/a (no core) rather than a number.

The same pair of numbers appears in the PDF report (File → Print / Report...). Note that this is the ratio at ignition only - the port opens up as the grain burns, so it is a check on the start of the burn, which is when the port is at its most restrictive.

Initial free volume

The Initial free volume line is the gas space inside the motor at ignition - every grain's port, plus the volume of the nozzle's convergent cone: 

Initial free volume: 7.59 in^3

The convergent cone is genuinely part of the chamber - gas fills it before the throat chokes - and it is not always a small correction. On the demo motor above it is 1.03 in³, or 14% of the total, and on a shorter, fatter motor it is more. Its size comes from the convergent half-angle; a motor saved before that field existed carries 0, which means "not stated" and falls back to the same assumed 45 degrees the Cross-Section view draws it at, so this figure always agrees with the picture.

Two things are not included, because BurnSim carries no geometry for them: any head-end ullage above the forward grain, and the gaps between grain segments. For a cored motor these are usually small. For an end burner they are not - see the caveat under What they assume below.

The figure follows the Imperial/Metric setting (in³ or cc). It is read at zero burn depth, like the port/throat ratio; free volume grows as the grain burns back.

This line was called "Initial core volume" before 4.0.0.18, when it counted the grain ports only.

Igniter mass

The tab gives two estimates of how much igniter this motor needs, from two published correlations built on different variables: 

CuO/Al igniter:  1.93 g  (by burning surface)
Free-vol igniter: 0.50 g  (by free volume)

Both are always reported in grams, whichever way the Imperial/Metric setting is set.

The figures above are the demo motor's: 76.5 in² of burning surface at ignition, and the 7.59 in³ of free volume from the section above.

Neither number supersedes the other, and they are not two attempts at the same answer. Each correlation is blind to what the other measures. Where they disagree is the useful part - see Reading the two together below.

By burning surface: the CuO/Al figure

This estimates stoichiometric copper(II) oxide / aluminium thermite, following the sizing model published in Reese, Wright and Son, "CuO/Al Thermites for Solid Rocket Motor Ignition", Journal of Propulsion and Power Vol. 29 No. 5 (2013), pp. 1194-1199 (doi:10.2514/1.B34771; a copy is hosted on Richard Nakka's site). The paper works through a dual-criteria model - the charge has to raise the propellant surface past a critical temperature and deliver a critical total energy to it.

The practical consequence is the part worth understanding: the thermite burns for a roughly fixed action time (about 75 ms, which the paper measured to be nearly independent of how much of it you use) and delivers a roughly constant heat flux while it does. So the energy that reaches the propellant scales with exposed burning surface area. The paper's own conclusion puts it directly: "because the parameter of merit for ignition is heat flux q, the surface area of the exposed propellant is of paramount concern".

Its Table 3 settles the point rather neatly. Two of the three test motors - the moon and BATES grains - had identical port volumes of 49.01 cm³ but different burning surfaces, and needed different charges (0.4819 g and 0.8198 g) in proportion to those surfaces. All three cases land on 0.0039 g of thermite per square centimetre, which is the constant BurnSim uses.

By free volume: the SP-8051 figure

The older and more widely known way of sizing an igniter, from NASA SP-8051, Solid Rocket Motor Igniters (Barrett, 1971), section 3.2.1.1.1. Plotting the weight of Alclo igniter pellets against motor free volume on logarithmic coordinates gives a straight line of slope 0.7: 

W = K x V ^ 0.7

with W in grams and V the motor free volume in cubic inches. The monograph leaves K to be read off its figure 10; Sutton's Rocket Propulsion Elements states it as 0.12, and puts the working tolerance at a factor of two either way. Sutton and Barrett are not two independent rules here - Sutton's igniter section draws on SP-8051.

This is an empirical fit, and the monograph is candid about what that costs: it "obviously makes the assumption that all pertinent motor variables vary in accordance with the free volume, and thus is a 'broad-brush' approach to igniter design". It was fitted on large military motors (FW-1, Skybolt, DM-14), and it is blind to how much burning surface it is lighting.

Note also that it was measured on Alclo pellets (35% aluminium, 64% potassium perchlorate), not on a CuO/Al thermite. It is a sizing estimate for an igniter charge in general, not a second opinion on the same thermite.

Reading the two together

Each model is blind to what the other measures, and each was fitted at a different scale:

  • The surface model is explicit that "gas phase heat release and mass diffusion effects are neglected" - it models heating the propellant surface, and says nothing about filling and pressurising the chamber. All three of its validation motors had free volumes between 49 and 52 cm³, so its data could not have detected a volume dependence even if one existed. All three had 3.8 cm cores; it is a small-motor model, offered as such.
  • The free-volume model is the opposite trade: large motors, purely empirical, and indifferent to burning surface.

For a cylindrical port of diameter d and length L, the surface figure grows as d×L and the free-volume figure as (d²L)0.7, so the ratio between them goes as d0.4 / L0.3. A wide, short port is volume-sized; a long, narrow one stays surface-sized however long it gets. That is the opposite of the common intuition that a long empty chamber must need more igniter - making a motor longer raises the volume figure only as L0.7 while raising the surface figure as L, so it always moves the balance towards the surface figure.

Port By surface By free volume Sized by
0.75 in x 9 in 0.53 g 0.32 g surface
1.9 in x 9 in 1.35 g 1.16 g surface
4 in x 12 in 3.80 g 4.02 g free volume
10 in x 12 in 9.49 g 14.49 g free volume

The crossover falls around a 4 inch port at ordinary lengths - which is roughly where SP-8051's data begins and where the CuO/Al paper's stops. Past it, the surface figure is the one being extrapolated. When the free-volume figure comes out the larger, the tab says so and tells you to size to the larger of the two.

What they assume

Treat both as well-founded starting points for your own testing, not as specifications. In particular:

  • The CuO/Al constant is calibrated against one propellant - the AP/HTPB/aluminium composite the paper tested. A propellant that is harder or easier to ignite will not match it.
  • It assumes the packing method the paper settled on (a sonicated mixture, loosely packed in paper). Igniter construction changes the result; a differently packed or differently confined charge does not behave the same way.
  • It was validated over roughly 500 g to 50 kg of propellant. Motors far outside that range are extrapolation.
  • Both are initial-geometry figures - surface area and free volume are read at zero burn depth, which is the state the igniter actually has to light.
  • An end burner reads as almost no free volume, because at ignition its grain fills the tube and the only free volume BurnSim knows about is the convergent cone. Real head-end ullage is chamber an igniter has to fill, and BurnSim carries no field for it. On that geometry treat the free-volume figure as a floor, not an estimate.

See also

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