Fueled by Math | How much fuel system do you need for your car? There’s an equation for that.

What Is Brake-Specific Fuel Consumption?

First, you’re going to need a few metrics to plug in to the equation. You’ll need a target horsepower number and the brake-specific fuel consumption (BSFC) of your engine–we’ll talk more about BSFC in a minute. You’ll also need to know the number of cylinders, the desired duty cycle of your injectors, your base fuel pressure and, if using forced induction, the boost pressure you’ll be running, if any.

So let’s break down each of these concepts so we know what this magic equation is looking for:

Target horsepower is easy. That’s how much power you want to make with your engine. If you don’t know precisely, well, that’s why you’re doing this exercise, so estimate high. In most cases, a good fuel system can run quite happily below its ideal power level far more reliably than it can if it’s being pushed beyond its limits.

Brake-specific fuel consumption is a bit more esoteric, so let’s examine what it actually is. BSFC is essentially a measure of the relationship of fuel input to power output. It’s one of the keys to this equation because we need to relate the resources going into the engine with the work we want it to do.

Precise BSFC numbers are only attainable on a dyno, but luckily estimations work pretty well for our purposes, and the differences between two different engines of similar configurations are actually fairly close. And, again, when estimating BSFC, it’s always fairly safe to guess high for your application.

This chart can give you some starting points for estimating BSFC based on your desired configuration:

• Normally aspirated gasoline: 0.45-0.50
• Normally aspirated E85: 0.63-0.70
• Forced induction gasoline: 0.60-0.75
• Forced induction E85: 0.84-1.05

Looking at that chart, you can see evidence of a couple things you probably already knew–specifically, that E85 or forced induction needs about 30% more fuel to create each horsepower and that a turbocharged E85 engine needs a fire hose of corn-based goodness pointed at it.

Working deeper into the equation, you should be able to figure out the number of cylinders you’re working with–if not, you’ve already read too far–which brings us to injector duty cycle.

What Is Injector Duty Cycle?

Duty cycle is a hotly debated topic on the internet, but the best advice is going to come from the manufacturer of your chosen injectors. Typically, they’re going to tell you that your peak horsepower should be somewhere around 80% to 85% duty cycle of the injectors.

Duty cycle is basically an expression of the amount of time the injector stays open, so an injector operating at 85% duty cycle is staying open 85% of its max allowable time. Since we’re operating at more or less a constant pressure in a fuel-injection system, duty cycle is what controls the amount of fuel going into the combustion chamber.

So why not just get some badass injectors and run them at 50% duty cycle so you have plenty of reserve capacity? Well, technically that might work fine for max power, but injectors also have a minimum duty cycle as well, and getting a car to idle properly with those golf course sprinkler injectors would be tricky.

Other factors, like spray patterns and droplet size, are also figured into the mix when it comes to making power, and the manufacturers base their recommendations around what they consider to be ideal duty cycle, so pay heed.

But again, you have some wiggle room. If you think you might one day add more parts or E85 or even forced induction to your build and don’t want to buy a second set of injectors, do the math and see where your injector duty cycle lies in your current build. Then you can consult the manufacturer to see if running the injectors at that duty cycle is advisable.

With the numbers we have now, we can figure the amount of injector flow we’ll need. To do that, multiply the desired horsepower by the BSFC, then divide that by the number of cylinders times the duty cycle. Multiply the result by 10.5, and you’ll have the amount of fuel in cc/min that each injector will need to flow to produce that horsepower.

Or, if you don’t want to do the math yourself, you can just go to Deatschwerks’ handy fuel system calculator, plug in the numbers and let the computer do the hard work.

For example, say we’re looking to throw some additional performance at our 1991 Toyota MR2 Turbo. We’d like to bump our 250-horsepower Gen 4 3SGTE to crank out about 320 horsepower on E85. So, what kind of injectors are we going to need to get the job done?

According to the calculator–and using a BSFC of 0.85 (on the low side for BSFC but fairly safe for relatively mild builds and boost pressures)–we’ll need 693cc/min of injector flow to hit those power numbers with E85.

Now, most injectors are sized in 50cc/min increments, so a set of 700cc/min or 750cc/min injectors should do the trick nicely. If we were considering adding even more boost and more power, a set of 800cc/min injectors would flow enough E85 for 400 horsepower. Before purchasing, though, it would be worth a phone call or email to see how happy those would be at lower flow rates while we save bottlecaps for that giant turbo.

How to Size a Fuel Pump

Now we need to feed those injectors, and that means correctly sizing the fuel pump. Of course, there’s math for this, too, and it’s even simpler than the injector sizing.

To figure the pump liters per hour (lph) for your desired configuration, multiply your desired power by your BSFC, then divide the result by 1.585. This will give you the amount of fuel flow you need.

In our MR2 example, we multiply 320 horsepower by our 0.85 BSFC, then divide the result by 1.585. We see that we need 178 liters of fuel per hour to feed our engine.

Even at our fantasy 400-horsepower level, we still only need less than 220 liters per hour of E85, putting both our power levels well within the range of a 255 lph pump.

But is more pump always better? Well, no, and this is where you can get into more complicated areas than with injectors. Too much pump can be too much for both your fuel system and for the wiring feeding the pump, which was likely designed for a smaller capacity–not the overkill upgrade you’re trying to shoehorn in there. So when upgrading a fuel pump, make sure your electrical system is up to the task.

There’s also the matter of higher flow from a fuel pump overwhelming the fuel system and causing additional heat in the pump. This makes it a bit more complex to future-proof your build if you plan to employ additional power adders down the road, but there are solutions available.

For example, staged pumps that employ a single pump for normal driving and have the option of triggering additional pumps for track work or boosted configurations are a potential solution. Or modern brushless pumps that are more adept at running at multiple speeds can be employed for cars that see high-delta, mild-to-wild configurations.

So now you’re able to go out and choose the parts for your next fuel system based on math, not guesses. Have fun turning that fuel into thrust.