Six instruments
The engine knows nothing about being observed. These are bolted to it afterwards, and none of them may reach into the physics to make its own job easier.
1spec — the shop manual page
What I specified, and then, under a rule drawn across the middle of the page, what the program worked out from it. I look at this more than anything else in the project.
302 Windsor
SHORT BLOCK
bore x stroke 4.000 x 3.000 in 101.6 x 76.2 mm
displacement 301.6 cu in 4942 cc
compression ratio 9.50 : 1
clearance volume 72.68 cc
rod length 5.090 in lambda = 0.2947 (l/a = 3.39)
bore/stroke 1.333 oversquare
mean piston speed 15.2 m/s at 6000 rpm (nothing lives above 30)
CAMSHAFT
duration, advertised 266 deg in / 256 deg ex
lift at the valve 0.426 in / 0.425 in
lobe separation 110.5 deg
timing IVO 16 BTDC IVC 70 ABDC
EVO 52 BBDC EVC 24 ATDC
overlap 40 deg polite
---- everything above was specified. everything below came out. ----
CRANKSHAFT
forging cross-plane
firing order 1-5-4-2-6-3-7-8
the engine fires every 90 deg, eight times per cycle
WHAT EACH BANK HEARS
A manifold is not connected to an engine. It is connected to four
cylinders, and it only ever hears those.
right bank cyl 1 4 2 3 fires at 180 - 90 - 180 - 270
left bank cyl 5 6 7 8 fires at 270 - 180 - 90 - 180
LOPSIDED. Each bank coughs twice in quick succession, waits three
quarters of a turn, and coughs again. The two banks are out of step
with each other and the interference between them never resolves.
This is the burble.
WHAT IT COST TO GET THAT
A piston does not travel sinusoidally. Kill the once-per-turn term with
a counterweight and a twice-per-turn one is still there, and nothing
bolted to a shaft turning at ω can cancel a force at 2ω.
looking down the nose of the crank
O
.
.
O.....+.....O
.
.
O
shaking, at 3000 rpm, from 0.78 kg of reciprocating mass per bore:
force couple traces
primary 0 N 1032 Nm a circle counterweights take it
secondary 0 N 0 Nm nothing
NOTHING LEFT OVER. The secondaries cancel each other exactly, and
the primary couple traces a circle, which is a rotating imbalance, which
a counterweight can be drawn to oppose. The engine holds still. It will
idle at 600 rpm on soft mounts without walking across the bay.
This, and not the noise, is why Detroit forged crosses.
The engine fires evenly either way. Nothing at the flywheel can tell
these two apart. Run `windsor record` and `windsor record --flat`.The crank drawn in the middle is the view down its nose. Four throws at 90°, and the little diagram is why the secondary shaking forces cancel — which is the whole reason this forging exists and the reason the engine sounds like that is, strictly, a side effect.
2dyno — a water brake on the flywheel
A load applied to the flywheel, a speed held, torque read off, and the same sweep a magazine would have published in 1968. Nothing in the model was fitted to Ford’s figures, which is the only reason it is interesting that they agree.
302 Windsor — wide open throttle, water brake, 4.9 L
torque power BMEP vacuum advance peak p knock brake
rpm lb-ft Nm hp kW bar kPa deg bar index hold
975 290.4 394 53.9 40.2 10.01 0.5 19.3 43.2 4.98 0.0%
1482 304.6 413 86.0 64.1 10.50 1.3 23.2 49.4 4.58 0.0%
1985 307.1 416 116.1 86.6 10.59 2.5 27.3 54.9 4.50 0.0%
2486 303.2 411 143.5 107.0 10.45 4.1 31.4 60.2 4.54 0.0%
2987 285.8 387 162.5 121.2 9.85 5.8 35.5 64.4 4.59 0.0%
3490 272.2 369 180.9 134.9 9.38 7.7 36.1 63.4 3.98 0.0%
3991 256.5 348 195.0 145.4 8.84 9.8 36.7 62.4 3.52 0.0%
4493 238.0 323 203.6 151.8 8.20 11.8 37.2 61.1 3.14 0.0%
4994 216.9 294 206.2 153.8 7.48 13.8 37.8 59.6 2.81 0.0%
5495 195.4 265 204.5 152.5 6.74 15.5 38.2 57.8 2.52 0.0%
5996 172.5 234 196.9 146.8 5.95 16.9 38.6 55.9 2.25 0.0%
lb-ft hp
325 | ********** | 225
305 |******** ********** ooooooooooooooooooooooo| 211
284 | ******###oooo | 197
264 | oooooo ******** | 183
244 | ooooo ******* | 169
223 | ooooo ******* | 155
203 | oooo ****** | 141
183 | oooo ***| 127
162 | oooo | 112
142 | oooo | 98
122 | ooo | 84
102 | oooo | 70
81 |oo | 56
61 | | 42
41 | | 28
20 | | 14
------------------------------------------------------------
10 15 20 25 30 35 40 45 50 55 60 rpm/100
* torque o power # both
peak torque 307 lb-ft at 1985 rpm
peak power 206 hp at 4994 rpm
Ford rated the 1968 302-2V at 210 hp / 4400 and 295 lb-ft / 2400, gross.
Nothing here was fitted to those numbers.
The knock index is worst at the bottom of the range, where the end gas
has the most milliseconds to sit and cook. It is an index and not a
verdict; see the note in knock.hpp about whose engine the threshold
of 1.0 belongs to.The knock index is worst at the bottom of the range, where the end gas has the most milliseconds to sit and cook. It reports an index and not a verdict, and knock.hpp says whose engine the threshold of 1.0 belongs to.
3card — it draws its own picture
James Watt tied a pencil to a piston and let the engine plot its own pressure against its own volume. The trace is the work done, and the area enclosed is what you get to keep. Two hundred and forty years later I am doing it with hashes.
indicator card — 302 Windsor, cylinder 1, 2000 rpm
Pressure is logarithmic, so area is not work. The work is printed below.
WIDE OPEN THROTTLE
59.4 |#####
42.5 |. #####
30.4 |. ######
21.7 |.. #######
15.5 | ... ########
11.1 | .... ###########
8.0 | ..... #############
5.7 | ...... ##########
4.1 | ....... #.
2.9 | ......... .
2.1 | ........... ...
1.5 | ............ ..................
1.1 |...........................................................
0.8 | .......
0.5 |
0.4 |
0.3 |
0.2 |
bar +------------------------------------------------------------
TDC volume BDC
gross 11.99 bar pumping -0.08 bar net 11.90 bar peak 54.0 bar
THROTTLE CLOSED
59.4 |
42.5 |
30.4 |
21.7 |
15.5 |
11.1 |
8.0 |.##
5.7 |. ###
4.1 | . #####
2.9 | ... #####
2.1 | .. ######
1.5 | ................................
1.1 |.... ..... ##########.........................
0.8 |. ...... ############ .
0.5 |.. ....... ###############
0.4 | .. ........
0.3 | .. ...........
0.2 | ........................................................
bar +------------------------------------------------------------
TDC volume BDC
gross 0.97 bar pumping -0.93 bar net 0.03 bar peak 7.3 bar
# power . exhaust . intake . compression
Throttled, the engine spends 96% of everything it makes on
breathing. Wide open it spends 1%. That is the whole cost of
controlling a petrol engine by making it difficult to breathe, and it
is why a diesel, which throttles on fuel alone, is more efficient at
part load and barely more efficient at full.The second trace is the same engine throttled. It is not a smaller version of the first one — it is a different shape, and the difference between them is the engine spending almost everything it makes on suffocating itself. The numbers under that →
4record — two microphones behind two tailpipes
Nine seconds: idle, a cruise, one pull to the limiter, and back down onto the overrun. Both channels hear both pipes, quieter by the extra distance and later by the time sound takes to cross the gap. Nothing is widened or panned. The image is the geometry.
0:00 / 0:00
Switching cranks mid-playback is the entire thesis in one control. Nothing else about the engine changes.
5run — a gauge cluster wired to the sensors
The only instrument I cannot print here, because it is alive: rpm, manifold vacuum, cylinder pressure and knock index, redrawn in place while the engine idles in your terminal. Digits 0 to 9 open the throttle, space puts it on the floor, q gives it back.
6verify — the inspection sheet
Every number this project quotes, checked against something that existed before the code did. A derivative against finite differences, a burn rate against its own integral, a cylinder head against a flow bench, a firing order against the casting, a shock tube against its exact solution, and the thesis against a Fourier transform.
windsor — inspection
every number this project quotes, checked against something outside it
measured expected
THE LINKAGE
dV/dtheta against central differences rel 6.6e-11 < 1.0e-08 ok
piston acceleration, likewise rel 3.4e-10 < 1.0e-08 ok
piston travel at BDC is the stroke rel 0.0e+00 < 1.0e-12 ok
V(BDC)/V(TDC) is the compression ratio rel 1.9e-16 < 1.0e-12 ok
eight bores of it come to a 302 301.6 ci 301 to 302 ok
THE FIRE
burn rate integrates to its burn fraction rel 3.9e-07 < 1.0e-05 ok
and that fraction is the stated efficiency rel 0.0e+00 < 1.0e-06 ok
nothing burns before the spark so ok
gamma sags from cold charge to flame 1.246 1.2 to 1.28 ok
sound travels faster in hot exhaust 592.3 m/s 560 to 620 ok
THE BOTTLENECK
stock head at 0.400 in lift, 28in H2O 153.5 cfm 140 to 160 ok
published for stock C8OE-F castings: about 150 cfm there
and at the cam's own peak lift, 0.426 in 149.9 cfm 135 to 165 ok
effective area peaks and then goes flat 0.195 L/D 0.14 to 0.24 ok
and the factory cam lifts PAST that 0.2403 L/D at least 0.195 ok
0.426 in on a 1.773 in valve is L/D 0.24, past where the throat
stops the curtain growing. a cam is ground for area under the whole
curve, not for the one lift where the head is happiest.
blowdown into an atmospheric pipe chokes so ok
flow is signed, so reversion shows so ok
THE CAMSHAFT, AGAINST THE 1968 CARD
the card gives four events and two durations. the model is built from
centrelines and a separation angle, so all six of these are derived.
intake duration, advertised rel 0.0e+00 < 1.0e-02 ok
exhaust duration, advertised rel 0.0e+00 < 1.0e-02 ok
IVO, before top dead centre rel 3.6e-15 < 2.0e-02 ok
IVC, after bottom dead centre rel 0.0e+00 < 2.0e-02 ok
EVO, before bottom dead centre rel 1.1e-15 < 2.0e-02 ok
EVC, after top dead centre rel 2.4e-15 < 2.0e-02 ok
overlap rel 3.6e-15 < 2.0e-02 ok
a card quotes centrelines about the gas-exchange TDC, 360 deg away
THE CARBURETTOR
two 1.08 in venturis, area 11.82 cm2 11 to 12.5 ok
flowing at 3 inHg 304.8 cfm 270 to 320 ok
Autolite rate the 2100 at 287 cfm; the gap is its discharge
coefficient, which the geometry alone cannot know
WHAT WAS NEVER TYPED IN
302 firing order, from the forging 1-5-4-2-6-3-7-8 1-5-4-2-6-3-7-8 ok
5.0 H.O., same forging, later cam 1-3-7-2-6-5-4-8 1-3-7-2-6-5-4-8 ok
Ford changed the camshaft and nothing else, and so did this
the stock forging reads as a cross cross-plane ok
the billet one reads as a line flat-plane ok
the 302 fires every 90 deg so ok
so does the H.O. so ok
and so does the flat crank so ok
nothing at the flywheel can tell the two forgings apart
but the right bank hears, cross-plane 180-90-180-270 180-90-180-270 ok
and the right bank hears, flat-plane 180-180-180-180 180-180-180-180 ok
so one of them is lopsided so ok
and one of them is not so ok
WHAT IT COST
cross-plane secondary force cancels exactly so ok
flat-plane secondary force does not so ok
and it is this large 5000 N 4000 to 6000 ok
tracing a line: no counterweight opposes 1 0.95 to 1 ok
cross-plane primary couple traces a circle 0 0 to 0.05 ok
THE ENGINE, RUNNING
peak cylinder pressure 63.92 bar 45 to 70 ok
arriving after top dead centre 9.5 deg 8 to 20 ok
too early is knock and a hole in a piston; too late is heat out of the pipe
exhaust primary pressure swing, low 1.503 bar 0.3 to 3 ok
torque at 3000 rpm 285.8 lb-ft 250 to 320 ok
Ford rated the 1968 302-2V at 210 hp / 4400 and 295 lb-ft / 2400,
gross. the model makes 307 at 1985 and 206 at 4994.
THE FUEL
evaporating petrol chills the charge 23.69 K 20 to 28 ok
past stoich, less of it evaporates in time so ok
flame is quickest just rich of stoich 1.1 phi 1.05 to 1.15 ok
and a lean charge burns slower than stoich so ok
which is the whole justification for a vacuum advance
best torque is rich of stoichiometric so ok
real engines make best power near 12.5:1, which is phi = 1.18
WHAT STOPS THE ENGINE
knock is an index and not a verdict; these are all comparisons
worse at low rpm: more time to cook so ok
worse with sixteen more degrees of advance so ok
worse on 87 octane than on 94 so ok
worse at 11.5:1 than at 9.5:1 so ok
quieter on a rich mixture than on stoich so ok
so compression ratio, advance and octane are one decision, not three
WHAT THE PIPES ARE NOT
exhaust.hpp models a pipe as two delay lines, which is exact for a
LINEAR wave and clamps its source at Mach 1 because a blowdown is not
one. riemann.hpp is the nonlinear solver that says what that costs.
shock tube, against the exact solution rel 1.0e-05 < 2.0e-03 ok
and it invented no mass doing it rel 1.5e-14 < 1.0e-12 ok
and destroyed no energy either rel 7.7e-15 < 1.0e-12 ok
the blowdown front's speed down the pipe 1409 m/s 580 to 2500 ok
which is FASTER than sound ahead of it 137% over ok
sound in 900 K exhaust is 586 m/s, and a linear wave travels at exactly
that. this one does not, because it is a shock: its crest is hotter than
the gas ahead and is carried forward by the flow behind, so it outruns
its own front. it is why the crack of an exhaust is sharper at the pipe
than it was at the valve, and the engine here cannot reproduce it.
THE THESIS
half-order energy is the signature of a pulse train that repeats
every two revolutions instead of one. one bank, at idle:
cross-plane bank, half-order share 0.6983 at least 0.3 ok
flat-plane bank, half-order share 0.0009409 0 to 0.1 ok
the cross-plane bank carries far more of it 742x ok
that ratio is the entire project, and it came out of four throw angles
63 checks, all of them true.The last block is the one I care about. Half-order energy is the signature of a pulse train that repeats every two revolutions instead of one, and the ratio between the two cranks is 742 to one. That number is the entire project, and it came out of four throw angles.