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In the conceptual phase of the design, I am optimizing various entities of an airplane for the best cruising altitude and speed to reduce the cost, which also includes MTOW and fuel weight. Consider a scenario where airplane is undertaking a mission which will burn the entire mission fuel estimated. Now, in-flight it is very much likely that airplane is not able to fly at the best cruising altitude and/or speed. This will result in increase of fuel burn which might not be enough. How to tackle this problem of estimating fuel load for off-design conditions while optimizing the airplane?

One way to address this issue is to rely on the reserve fuel estimated for reserve mission such as loiter time. But, it might happen that airplane has to rely on the reserve fuel and due to increase in fuel burn during cruise, reserve fuel is less for loiter time. I don't think this is a desirable condition. Another way is to optimize the airplane for worst scenario. Now, the question arises what is that worst scenario. Is it flying at the cruise ceiling (cruising altitude and cruise ceiling are different) or something else?

Let me know how to address this problem. Thanks in advance!

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Very few airplanes have been used the way they were designed for.

From the trainer B.E.2 (which was abused for reconnaissance missions early in WW I) to the interceptor F-104 (which was used as a ground attack plane later), there are numerous examples. And for every mission that is still within the capabilities of one design you can think of numerous others that aren't. Therefore, dimensioning for the worst possible mission is an exercise in futility.

If an airplane carries too much fuel, it will be less economical. If it has too much strength built in, its structure will be too heavy. If the engines are more powerful than needed, it will have poorer fuel economy. In the end, every design can only fill its niche. But there are some principles which make some designs more useable:

  • Since regulations require a minimum number of flight attendants depending on the number of passengers, small passenger airplanes come with 19 or 50 seats but rarely with 23 or 55.
  • To be able to fly all domestic US routes, the more successful designs will have enough range to fly to Hawaii from airports at the West coast. If maximum range with full payload falls shorter than that, the design will be less versatile for US carriers.
  • Since air temperature is constant in the stratosphere, the most economical flight altitude is in the tropopause. Fly lower and you will not make full use of the cooler air above, fly higher and wing size and engine thrust will be less than optimal. Exceptions apply for business jets which like to fly above all other traffic.
  • Redundancy requires at least two engines, and maintenance cost demand to keep the number of engines as low as possible. Therefore, except for the really large airliners, the most successful ones all have just two engines.
  • In order to offer one of the fastest connections on a specific route, the reference cruise speed of long-range airliners is traditionally set at Mach 0.85. Fly faster and Mach effects will decrease fuel efficiency (demanding thinner airfoils and/or more wing sweep), fly slower and your design will drop from the first page of connections.

If you wonder how much a deviation from optimum airspeed will reduce range, I plotted that for a subsonic design (transsonic airliners will bump into steep drag increases with only a small increase in Mach, so this diagram does not apply to jets). I used a quadratic polar which gives a good approximation of reality.

Range reduction over airspeed

Range reduction over airspeed. Blue line: L/D at the specified speed. Red line: Range relative to optimum. The optimum speed in this case is 84 m/s. I also assumed constant engine efficiency over speed, so range purely depends on L/D.

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  • $\begingroup$ One also needs to factor IFR reserve regulations into any range calculation. $\endgroup$
    – StephenS
    Aug 4, 2021 at 20:20
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Are you designing a new airplane? If I understand the question correctly, For a normally aspirated engine, the engine is most efficient when the throttle is fully open at a particular altitude, where it produces approximately 65% -75% power. Therefore the airframe with respect to wing design, angle of incidence etc should be matched to give the best lift/drag ratio at that altitude. You will have to consult with the engine manufacturer to establish what that altitude is. Your choice of propeller is also going to have to be factored.

Then you calculate the fuel reserves accordingly.

Fuel reserves are calculated according to legal requirements of the country in which the airplane is registered and also in which it is operating. This varies according to the type of aircraft and the operation. For instance the minimum legal reserves are different for a passenger jet on a commercial flight, to a single engine airplane being operated on a VFR flight in the private category. Most countries laws are similar but there might be small variations, and they all have to satisfy ICAO standards if the country is an ICAO member state.

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    $\begingroup$ thanks for your answer! I am just curious to know how airplane designers estimate reserve fuel in the initial phase of the design. I have a rough approximation of how thrust and efficiency varies with altitude and speed. The plane is optimized for the best cruising condition, including reserve fuel which is not for off-design condition. This leads to least fuel, but there should be some extra amount of fuel to accommodate off-design cruise conditions, right? So, I wanted to how to do that. $\endgroup$
    – Pavan
    Mar 7, 2021 at 5:26
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    $\begingroup$ How do the airplane designers estimate additional fuel needed, along with the fuel for the best condition? If the fuel provided is for only for the best condition, then there won't be any space for additional fuel $\endgroup$
    – Pavan
    Mar 7, 2021 at 5:38
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    $\begingroup$ @Pavan Use the fuel reserves mandated by the prospective operator. For airliners that would be detour to the nearest alternative plus 30 min loiter. In the end, range is what is possible without reserve fuel, including expected winds aloft. Tank capacity is usually large enough so that payload can be traded for additional fuel. $\endgroup$ Mar 7, 2021 at 7:09
  • $\begingroup$ @PeterKämpf, thanks for your answer! I am considering the reserve fuel mission. I was doubt whether that would be enough or not. $\endgroup$
    – Pavan
    Mar 8, 2021 at 8:06

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