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I was looking for sfc per throttle setting of an engine. I was not getting the performance data of that engine. So is there any way to calculate it by formula?

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  • $\begingroup$ It's going to depend on the load put on the engine. RPMs alone don't tell anything about it, other than the average torque generated by the engine equals the load resistance at this RPM (or else it speeds up or slows down). $\endgroup$ Apr 17, 2023 at 13:40

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The variation of TSFC vs. Thrust (as you vary throttle) for a jet engine (at a given altitude and airspeed) is usually called a 'thrust hook'. So you will similarly hear a plot of BSFC vs. Power for a piston engine called a 'power hook'.

Piston engines can be a bit more complex because what happens with the variation of throttle depends on what kind of propeller you have (fixed pitch vs. constant speed).

The (mechanically more complex) constant speed prop is a lot easier to analyze -- you already know the RPM. Consequently, a curve depicting throttle variation (at a fixed flight condition) can be readily constructed.

For a fixed-pitch prop, the propeller (load) determines the relationship between power and RPM (at a given flight condition) as throttle is varied. Different props will have different load curves.

Consequently, you need a more complex model for the engine to be able to analyze it connected to an arbitrary fixed-pitch prop. This model is not just a curve, it is a map. Google 'bsfc map' and you will find plenty of examples.

Although some engine parameters are easy enough to come by (RPM, bore, stroke, number of cylinders, compression ratio, etc) -- those are not enough to construct an accurate model of engine performance. To do that, you need to know detailed information about the friction between the rings and cylinders, in the bearings, how the valves are operated, etc. All of these things contribute to losses that are important for determining the engine's fuel efficiency (and how it varies with speed and power).

All those factors are typically determined empirically (through test) -- not just known from analysis.

So, your best bet is to find some engine performance charts for your engine -- or a similar engine. What engine(s) are you considering? Will you be using a fixed pitch or constant speed prop?

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You have to know the horsepower being generated at a given throttle setting, which means you need the manifold pressure and RPM, and using those values, derive the horsepower that results from the engine's power chart. So without a power chart, or some other data that tells you what HP is achieved at some throttle opening, you are stuck.

If you know the HP being created, and it's a carbureted air cooled piston engine, you can use an SFC value of 0.45 lbs/hp/hr as a ballpark number. So if you know that the throttle setting is giving you 100 HP, at some manifold pressure and RPM, you can assume the fuel burn is 45 lbs/hr, or 7.5 US Gal/hr. This is about what the cruise fuel consumption is for a 140 hp Lycoming O-290 that makes about 105 hp at 75% cruise.

For a fuel injected engine you can reduce the value to a bit lower, say .42/lb/hp/hr.

Car engines are in the high threes, and diesels are in the low threes. Two strokes and turboprops are thirstier, in the 5-7 lb/hp/hr range.

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  • $\begingroup$ Yes finger trouble. Thanks for the catch. $\endgroup$
    – John K
    Apr 17, 2023 at 12:50
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My prior answer assumed you were looking at a piston engine. This answer will reflect your update to interest in a turbofan engine.

You are interested in calculating the thrust hook (TSFC vs. Thrust as a function of throttle) at a given flight condition (Mach and altitude). Here is an example for a turbofan engine:

enter image description here

As you can see, at each flight condition (numbered line), SFC and Thrust vary along a curve (as you vary throttle). Note that these hooks do not include the flight idle condition (very low throttle). Flight idle would show SFC getting substantially worse very quickly.

There is no simple equation to calculate a thrust hook.

Instead, you typically use a computer program capable of performing off-design cycle analysis. Usually a first undergraduate course in propulsion will discuss on-design cycle analysis (first ideal, then non-ideal). Off-design cycle analysis is usually not discussed until a second undergraduate course or a graduate course in propulsion.

In on-design cycle analysis, we analyze the engine at a single design point (flight condition and throttle setting). This analysis allows us to size the engine to meet a design thrust. Sizing the engine in cycle analysis means calculating the flowpath areas at each station (inlet, compressor inlet, compressor exit, combustor, turbine inlet, turbine exit, nozzle, etc).

In off-design cycle analysis, we take the fixed engine from the on-design analysis (leave the areas and other properties fixed) and then model its operation at different flight conditions and throttle settings.

An off-design cycle analysis requires compressor, fan, and turbine maps. These are performance models of the turbomachinery components. I.e. not just an on-design compressor pressure ratio and efficiency, but a map of how compressor pressure ratio and efficiency vary as functions of corrected speed (RPM) and corrected mass flow (compressor face Mach number).

At every operating condition, we solve to find the equilibrium point where the compressor and turbine are balanced (power in equals power out) at the same speed (RPM) and mass flow. This is an operating point.

At each flight condition, we calculate an 'operating line'. This is the locus of all the operating points at that flight condition (as we vary throttle). This operating line is usually plotted on the compressor or fan map, but once you can calculate an operating line, you can also calculate a thrust hook.

If you have thrust hooks at a wide variety of flight conditions, (i.e. a complete performance model of the engine), you have an 'engine deck'. A deck is the industry term for the data package an engine company would provide to an airframe company to use when designing and analyzing their aircraft. Back in the day, it was a deck of punch cards. Today, the 'deck' name persists, but an engine deck is usually supplied as a computer program provided from the engine company to the airplane company.

A bunch of scaling is often performed for engine data. This isn't exactly non-dimensionalization (as the results are still dimensional quantities), but it works similarly. Each parameter is 'corrected' in this process. Mass flow becomes corrected flow. Thrust becomes corrected thrust. Compressor and turbine maps are usually provided in corrected form.

With some limitations, an engine's operating line at different flight conditions can fall onto a single operating line when written in corrected properties. Consequently, if you have a corrected operating line, you may be able to get to a hook at many flight conditions (i.e. a deck).

If you have a corrected operating line, 'dimensionalizing' that data for an engine will be the closest you can come to a simple equation for calculating a thrust hook. It still isn't easy -- and that line was generated with sophisticated analysis (off-design analysis) that was in turn built on sophisticated models of the turbomachinery (maps). Neither of those steps submit to simple analysis.

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