Optimum Flying Speeds
This section relates to Piston Engines and TurboProps only. Sorry Jet Jockeys!
Best Range Speed
Best Glide Speed
Best Endurance Speed (Piston Engines)
Minimum Rate of Descent Speed
Best Rate of Climb Speed
Max Angle of Climb Speed
Endurance Speed for TurboProps
Summary
Max L/D = Min Drag speed = Best Glide Speed = Best range speed
Definitions
GFC=fuel used/unit time
SFC=GFC/shp
RANGE
An aircraft is flown for range such that it travels the maximum distance using the minimum fuel. This aim can be expressed by the equation:
Efficiency=work out/work in=weight*distance/fuel used
Specific Air Range (SAR) is the distance travelled per unit of fuel burnt ie.
SAR=distance travelled/fuel used
If the SAR equation is divided top and bottom by time:
SAR=(distance travelled/time)*(time/fuel used)=TAS/GFC
From the above definitions GFC=SFC*power therefore:
SAR=(TAS/power)*(1/SFC)
Therefore given a certain weight and still air to maximise range we must maximise our airframe efficiency (TAS/POWER) and engine efficiency (1/SFC). Now if we look at the graph above we see that the maximum value of TAS/power is the point where the tangent from the origin touches the curve. This speed coincides with Vmd for the following reason: Power required is a product of drag and TAS thus:
Power=drag*TAS and therefore TAS/Power=1/drag
**Note the graphs are drawn for sea level where TAS=EAS
Effect of Altitude
When flying at Vmd the aircraft will experience constant drag because Vmd is an indicated airspeed (compressibility effects ignored). As altitude increases so does TAS at a constant IAS. Power required also increases because Power=drag*TAS and thus the TAS/Power ratio remains the same. Given this the only effects altitude has, is in respect to the engine efficiency. For turboprops you must climb to the altitude where Max Cruise RPM gives you Vmd.
Effect of Wind
Wind has the effect of moving the origin of the TAS vs Power graph. Headwind moves the origin to the right and the new tangent will give a slightly higher speed. The converse is true for a tailwind. These effects are fairly small and adjustments need not be made unless the headwind exceeds 25% of TAS or a tailwind exceeds 33% of TAS.
In Practice
In practice aircraft will be flown at a speed slightly higher than Vmd for two reasons. (a) Variation of TAS/Power near Vmd is negligible and will allow a faster flight without undue loss of range. (b) When flying at Vmd it is too easy due to turbulence or manoeuvres to fall behind the drag curve and then require a higher power and fuel wastage to return to the desired speed.
GLIDING
The aim in gliding is to achieve the least height lost per unit of distance across the ground. That is the maximum of Glide Distance/Altitude. Another way to think of this is we want the minimum ratio of rate of sink to forward airspeed. The next section will explain how RoD is related to the Power vs TAS graph. Given that RoD is directly related to power and therefore airspeed, we can use the tangent from the origin of this graph to the curve to get a maximum of airspeed/RoD. If we multiply this top and bottom by time we get Distance/Altitude which is what we are trying to maximise in a glide. Since power is directly related to RoD we can say we are maximising TAS/Power. Power = Drag*TAS therefore we are maximising TAS/(Drag/TAS)=1/Drag. 1/Drag is a maximum at minimum drag. In level flight lift is equal to weight. In normal angles of glide, lift is almost equal to weight. Only at high dive angles does it vary considerably; therefore throughout the entire range of possible flight speeds,the lift is essentially constant at a constant weight. The L/D ratio would therefore only vary with drag and thus would be a maximum at minimum drag. Therefore max glide speed can be said to equal maximum lift on drag speed.
Summary
Min power speed = Best endurance speed(Piston Engines) = Min RoD Speed
Min RoD
If you read the Max Excess Power section you will find that max Rate of climb occurs at max excess power. With no power the X-axis can be thought of as power available. Instead of trying to maximise the difference in power available to power required we are trying to minimise it. This occurs at min power speed. Thus minimum Rate of descent will occur at min power speed.
Endurance
We are trying to maximise our time airborne therefore we must minimise fuel flow. Fuel consumption is proportional to power setting, therefore maximum endurance will occur at minimum power speed.
In level flight just enough power must be made available to match the amount of power required for the airspeed desired. This is achieved by manipulation of the power controls. At less than maximum speed, more power is available than is required for level flight. This additional power is climb capability and the rate of climb is determined by the amount of additional power available.
The graph shows that max rate of climb occurs at Vy which is the point where we have maximum excess power. An increase in altitude moves the Power available line down. Absolute ceiling is where the two lines are tangential and there will be only one speed that will maintain level flight. An increase in weight moves the power required line up and thus would reduce the excess power and thus the rate of climb.
Algebraically Rate of Climb = Excess Power/Weight*"a constant to convert units"
This graph is derived from the horsepower vs velocity graph and is RoC plotted against velocity. You can see Vy marked at the top of the graph. A line tangential to this curve from the origin gives us the greatest ratio of vertical speed to horizontal speed and thus is the maximum angle of climb speed (Vx).
As in a piston engne aircraft minimum fuel flow is required and this is acheived when the product of power required and SFC is a minimum. The airframe demands least power at minimum power speed, plus about 10kts for control, at as low an altitude as possible. The engines are most efficient at Max Continuous RPM at a high altitude and a high TAS. Due to these conflicting requirements a compromise is reached at a medium altitude at about Vmd acheived by retarding the throttles. The actual altitude chosen is not critical because there are equally good reasons for flying higher or lower.
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