Light Jet Thrust Formula (#1)

For determining minimum static thrust required for non flat-rated turbofan and turbojet engines.

As temperature and or altitude increases, the amount of thrust produced by an engine will subsequently decrease. On larger turbines, flat rating is available to supply rated thrust above sea level and ISA. For smaller engines that may not have the thermodynamic capacity to flat rate, the designer must take into account the degradation of thrust. Failure to do so will result in unsatisfactory performance, inability to meet expected book values and possible payload restrictions.

The simple fact is as engines get larger, the weight of passengers becomes less of a fraction of the static thrust. Those who wish to build cabin class transportation aircraft are probably going to find their optimum engine (or engines) in the 2000lb thrust class or larger. Use of small jet engines under 500lbs thrust is therefore likely to be associated with very light multi engine craft, experimental/test vehicles and unmanned aircraft. Development of small jet engines however, should not be deterred by market analysis that may not fully understand the different potential uses beyond business and high-end general aviation. Too often advances are cut short by the opposite nature of engineering and profit, which work on completely different time scales.

The urge to use as small an engine as possible should be avoided when building light jet aircraft for the simple fact that passengers cannot be reduced in weight. Smaller engines can operate closer to their optimal TSFC at cruise altitude, but like all of aviation, there has to be a tradeoff for other flight envelopes. Therefore if one wishes to have a 4 place jet with a 200 lb allowance for each passenger, using twin 400 lb thrust engines for a total of 800lbs will provide a 1:1 thrust to payload ratio. This number will gradually change as airframe, fuel, avionics and interior is added. By the time a weight of say 3200lbs is reached (1600lbs empty weight, 800lbs payload and 800lbs fuel…very minimal levels), the total thrust to weight has declined to 4:1. This figure is at sea level on a standard day. Take the same aircraft to Colorado Springs at 65 degrees and the thrust to weight balloons to 5:1. Each pound of thrust has to push over 5lbs of aircraft, thus increasing takeoff distance, time to climb, and fuel consumed over a given stage. Humidity and air pressure may also conspire to rob the engines of performance.

The following formula is very simple as it is meant to be a rough estimate to warn a designer of low thrust levels at a nominal altitude of 6,000 ft MSL and 65 degrees. This altitude also equates to approximately 0.785 with respect to air density at SL ISA. But we’re conservative and/or lazy so the easy to remember 0.75 ratio is the rule of thumb to remember. The thrust lapse rate is based on a low bypass turbofan engine (less than 3:1) and will vary with fan size, nozzle design and turbine temperature. Your engine will vary so consult the appropriate manufacturer tables when advancing beyond the initial planning stage of your design. By using a reduced thrust computation when setting gross weight, unpleasant surprises can be avoided while in the flight test stage.

Tr₁/.75=Tr₂

Thrust to weight ratio 1 = A/C weight divided by thrust at sea level, ISA.

Thrust to weight ratio 2 = A/C weight divided by thrust at roughly 6000 feet MSL, ISA.

If you really want to scare yourself, multiply 0.75 by the static thrust of your selected engines (assuming they are not flat rated) and see what number you get!