Formula
Injector flow is the fuel the engine needs, split across the injectors, with the duty cycle kept under 100% so the injector is not open the whole time. Brake specific fuel consumption is pounds of fuel per horsepower-hour. Naturally aspirated gasoline is often about 0.50. A boosted gasoline engine is often about 0.60 because the mixture is richer to control knock. The BSFC field is that gasoline number. E85 multiplies it by 1.35 unless you edit the factor. That factor is the practical range of about 1.3 to 1.4, not the raw stoichiometric ratio of 14.7 / 9.8. Methanol uses 2.2 and a density of 0.79 g/cc. U.S. DOE figures put methanol near 6.63 lb/gal, about 0.79 g/cc.
lb/hr each = (HP × BSFC × fuel factor) / (injectors × duty)
cc/min = lb/hr × 7.5599 / density
new flow = rated flow × √(new pressure / rated pressure)
duty % = pulse width ms × RPM / 1200
7.5599 is 453.592 grams in a pound, divided by 60, rounded. At 0.72 g/cc the conversion is about 10.5, which is the familiar gasoline factor. Grams per minute are lb/hr times 453.59237 / 60. Engine fuel demand is horsepower times the effective BSFC. The per-injector figure is larger than that demand divided by the injector count, because the duty cycle is under 100%.
Fuel pressure changes flow with the square root because an injector orifice follows that relationship. The rated pressure on the page defaults to 43.5 psi, which is 3 bar in the workshop convention used here: 14.5 psi per bar, and 100 kPa per bar. A rising-rate regulator that adds 1 psi of fuel pressure per psi of boost holds the injector differential at the base setting. Without it, the differential falls as boost rises and the injector flows less than the base rating at the same pulse width.
Pulse-width duty on a sequential four-stroke uses two revolutions per cycle, so the cycle is 120,000 / RPM milliseconds. Ten milliseconds at 6,000 rpm is half of the 20 ms cycle, which is 50%. Above 85% is a warning. Above 100% is called out as static. That mode is allowed to exceed 100% so the warning can appear. The sizing modes are not: they stay inside 50% to 95%.
Use crank horsepower. A chassis-dyno figure is wheel horsepower, and dividing it by a drivetrain efficiency is only an approximation of the crank number the BSFC was written against. The final injector, the dead time, and the fuel table are a tune. A wideband is how you know the engine is not lean under load.
Worked examples
400 hp, BSFC 0.50, eight injectors, 80%, gasoline at 0.72 g/cc. 31.25 lb/hr and 328.1 cc/min each. Demand is 200.0 lb/hr.
500 hp, BSFC 0.60, four injectors, 80%. 93.75 lb/hr and 984.4 cc/min each.
The same 400 hp V8 on E85. Factor 1.35 makes the BSFC 0.675. 42.19 lb/hr and 408.89 cc/min at 0.78 g/cc.
42 lb/hr rated at 43.5 psi, run at 58 psi. 48.50 lb/hr.
Six injectors, 60 lb/hr, 85% duty, BSFC 0.60. 510.0 hp.
6,000 rpm, 10 ms pulse. 50.0% duty. The cycle is 20.0 ms.
Reference
cc/min factor is 7.5599 divided by density. Gasoline at 0.72 g/cc is 10.50. E85 at 0.78 is 9.69. Methanol at 0.79 is 9.57.
| Case | lb/hr each | cc/min |
|---|---|---|
| 400 hp NA gasoline | 31.25 | 328.1 |
| 500 hp turbo gasoline | 93.75 | 984.4 |
| 400 hp NA E85 | 42.19 | 408.89 |
Questions
What size injectors do I need for a horsepower target?
Divide horsepower times BSFC by the number of injectors and the duty cycle you are willing to use. A 400 hp gasoline engine at a BSFC of 0.50, eight injectors, and 80% duty needs 31.25 lb/hr each, about 328.1 cc/min at 0.72 g/cc. Pick the next size up from that figure. It is still an estimate until the engine is tuned on a wideband.
How do I convert lb/hr to cc/min?
Multiply lb/hr by 7.5599 and divide by the fuel density in g/cc. 7.5599 is 453.592 grams per pound divided by 60. At 0.72 g/cc the factor is about 10.5, which is why gasoline lb/hr times 10.5 is the usual cc/min figure. E85 at 0.78 g/cc uses a smaller factor. The page shows the factor it used.
What injector duty cycle is safe?
Sizing at 80% leaves room for injector opening time and heat. This page allows 50% to 95% and warns above 85%, but it still calculates. A pulse-width result above 100% is static: the injector would have to stay open longer than the cycle, which it cannot.
Does raising fuel pressure increase injector flow?
Yes, by the square root of the pressure ratio. An injector rated 42 lb/hr at 43.5 psi flows about 48.50 lb/hr at 58 psi. On a boosted engine with a 1:1 rising-rate regulator, the differential across the injector stays at the base pressure. Without one, boost subtracts from that differential.
How much bigger do injectors need to be on E85?
E85’s stoichiometric air-fuel ratio is about 9.8 to 1, against about 14.7 for gasoline, so the engine needs more fuel mass. This page multiplies the gasoline BSFC by 1.35 by default. A practical range is about 1.3 to 1.4. The same 400 hp V8 goes from 31.25 lb/hr to 42.19 lb/hr per injector.
What is BSFC?
Brake specific fuel consumption is the fuel mass the engine uses per horsepower per hour. Naturally aspirated gasoline engines are often near 0.50 lb/hp·hr. Supercharged and turbocharged gasoline engines are often near 0.60 because the mixture is richer under boost. The field on this page is that gasoline figure. E85 and methanol multiply it.
Do I need a tune after changing injectors?
Yes. The ECU has to be recalibrated with the new injector data, or the engine will not deliver the flow this page estimated. Confirm the result with a proper tune and wideband air-fuel monitoring. Running lean under load can destroy an engine.
Sources
- John B. Heywood, Internal Combustion Engine Fundamentals. Brake specific fuel consumption is the fuel mass flow divided by brake power. The 0.50 and 0.60 presets are workshop gasoline figures in that tradition, not a measurement of one engine.
- Orifice flow scales with the square root of the pressure difference. The pressure mode is that relationship and nothing else.
- U.S. Department of Energy, Alternative Fuels Data Center, fuel properties. E85 density is taken as 0.78 g/cc. Methanol is about 6.63 lb/gal, taken here as 0.79 g/cc. Gasoline density for the common 10.5 cc/min factor is 0.72 g/cc. The constant 7.5599 is 453.592 / 60.
- Stoichiometric air-fuel ratio is about 14.7 for gasoline and about 9.8 for E85. The default E85 factor of 1.35 is the practical sizing band of about 1.3 to 1.4, not 14.7 / 9.8.
- Related pages: turbo size, displacement, compression ratio, gear ratio, and the quarter-mile calculator for an ET and trap-speed estimate from the same kind of horsepower figure.