P Over D

Lift to drag ratio or L/D is the figure that many crucial aerodynamic criteria are measured by. When soon-to-be pilots study for the FAA written exam, they pore over diagrams of L/D curves and where the most efficient speeds are. They see how glide ratio, climb speeds and best endurance speeds are determined. They see how L/D varies with angle of attack and altitude. They see all this information presented before them and yet are only getting half of what they need to know operationally. The number we’ll be exploring today is the P/D, or payload to drag ratio.

First, what does L/D mean aerodynamically? Quite simple; it means that you have the lowest amount of drag for your given weight. Hence, lift (holding up your weight) over drag. If your L/D went from 10 to 5, it would mean that you are producing more drag for your given weight (whether it is parasite or induced drag depends on the type of speed change). Speaking in terms of the airplane itself, L/D is the determining factor for efficiency. Sailplanes have extremely high lift to drag ratios and are often touted as being the most aerodynamically efficient winged craft on the planet. Sailplane-type aerodynamic efficiency means that making 180 degree turns with no engine at 300 feet above the ground and staying aloft in thermals for hours is completely normal. On the other hand (and there always is another hand), the downside to measuring an airplane’s worth by its L/D ican limit its usefulness. While a sailplane can play in ridge lift for the better part of a day, it’s doing it at the expense of two very important variables: payload and speed.

P/D is the transportation equivalent of the aerodynamic L/D. While everyone talks lovingly of L/D, they almost never ask the question I always ask: “What are you lifting?” It’s similar to me telling a big rig driver that I’m more efficient because I get 100mpg on my moped and he only gets 6mpg. Sure I’ll feel like a eco-hero, but the missing part of the equation is what is my moped can carry and how fast. I weigh around 200lbs, or 0.1 tons, so we can assume that as the moped’s payload. The 18 wheeler on the other hand has a payload of roughly 48,000 lbs or 24 tons. My moped (wide open throttle and downhill with a tailwind) can hit 40mph while the truck can easily cruise over 70mph. What would you rather have deliver 24 tons of groceries to your store from a warehouse site 200 miles away? One truck that takes just under 3 hours, or 240 mopeds that will take 7.5 hours?

The same principle applies to aircraft. Most people buy airplanes for speed. They want to save time over driving or taking the airlines. They want to be on their own schedule. They sometimes just want to be able to say “I cruise at Mach 9.5” to their friends who all cruise at Mach 9.2. Very few people buy powered airplanes for a distinct lack of speed. There is also another camp that values payload over blistering speed. The ability to lift a lot of people or a lot of cargo is critical for airlines and charters in order to make a profit. It counts for general aviation as well since quite frankly, many of the standard “4 place” airplanes are really “2 people plus a couple bags” craft with respect to payload and full tanks. Many planes have been wrecked and too many people killed because pilots failed to fully understand the significance of this nebulous limitation.

Time to compare L/D to P/D. The Schwiezer SGS 2-32 glider has a reported L/D somewhere between 32/1 and 36/1. For it’s gross weight of 1340 lbs, it will be producing between 38 and 42 lbs of drag. Incredibly low numbers thanks in part to it’s low drag fuselage and high aspect ratio wing. This max L/D is achieved at a speed of 45 knots, which is very slow for transportation considerations and totally unusable for any powered airplane’s cruising flight. Assuming 2 large men weighing 250lbs each are on board, the payload is 500 lbs. P/D is between 13.9 and 15.6, which are the real numbers we want. For each pound of drag, the aircraft is carrying an average of 14 lbs of payload.

P/D ratios that high will not be commonplace in powered aircraft simply because they are much heavier in structure and can’t carry as large payload with respect to their maximum weight. A very heavy-lifter, the Boeing 747-400F has an average L/D of 17.5 at 35,000 feet and normal cruise speed, while maximum payload is listed as 248,000 lbs. Assuming an late-in-cruise weight of 700,000 lbs, drag would be 40,000 lbs and P/D therefore is 6.2. Closer to home for many of us, the Cessna 172 has an L/D in the region of 9.0. At 2400 lbs gross weight, the resultant amount of drag is 267 lbs. Assuming 3 people are on board who weigh 200 lbs each, the P/D works out to 2.25. Most light aircraft will end up reasonably close to this number, varying by the number of seats on board.

Why is P/D important to designers? Because while purist pilots may love airplanes, airlines quite frankly couldn’t care less about the aircraft itself as long as it does 3 things:

  1. Doesn’t crash randomly.
  2. Is reliable.
  3. Turns a profit.

If you wish to build military fighter/attack aircraft, the desires are slightly different:

  1. Doesn’t crash randomly.
  2. Is reliable.
  3. Carries a lot of weapons.

And if you want to build a business jet…well, you get the idea. The only category of aircraft where payload can be ignored somewhat is the personal pleasure craft, such as certain experimental and ultralight aircraft. They aren’t made to make money, they’re made to enrich the builder/owner’s life. On the other hand, if an airliner has a beautiful shape that inspires poets worldwide, sets speed records and adds alleged prestige to the company, that won’t save it from being cast aside in favor of something more pedestrian but economical (and yes, I was referring to that supersonic work of art, the Concorde).

The more an aircraft weighs empty equates to more structure and materials which directly leads to more cost. The more an aircraft weighs empty, the less it can carry in fuel and payload if it’s maximum takeoff weight is not also adjusted upwards. So not only will it cost more to buy, but it produces less per trip in terms of revenue. From an economic standpoint, an airplane that has lower than average aerodynamic virtues but exceptional carrying capabilities will be more desirable than a craft with a high L/D but limited payload. This explains the ongoing interest with composites to reduce airframe weight without sacrificing strength.

P/D is just another number that can help you analyze performance in a practical manner. For instance, if you’re looking to buy an airplane for personal use, consider who and what you want to take with you. A super efficient powered glider that has only one seat is pointless if your goal is to carry your family on short trips. Likewise, if you find an airplane that has a very high cruise speed but it requires you to lay flat like a Mercury astronaut, that won’t make the kids very happy, especially since there are no windows to see out of. Like everything else in aviation, its a balance with your needs as the fulcrum.

Next time, we’ll talk about all the “best” speeds and why they aren’t speeds.

What Are You Lifting?

Mention aerodynamic efficiency to most pilots and designers and you’ll probably hear the phrase “lift to drag ratio” within a sentence or two. Common aerowisdom dictates that for maximum efficiency, a high lift to drag ratio is required of an airframe. Of course, like most truths it is true and false at the same time. I’ll attempt to explain without going into a thesis level discussion as to why a high lift to drag ratio (L/D) is not the be-all-end-all of aerodynamic efficiency.

Long thin wing of a 757-200. Design is great for reducing drag on transcons, plus blended winglets provide ample space to advertise.

Now I’m going to I make designers start ripping out their hair and turning over their drafting boards…wait, it’s almost 2012…turning over their CAD mainframes. This is not exactly a law but it should be, and it will help many budding aircraft designers achieve their intended goals:

Any lift to drag ratio without a measure of what is being lifted is not operationally useful. 

(and in plain English)

Lift to drag is useless unless you’re lifting something useful.

Sorry, but I had to say it. Obsession over a high L/D is great if you want your airplane to look like a U-2. It’s not great if you want to be able to land it without pogo sticks under the wingtips. The first question you should be asking is “What do I want to lift?” More accurately, “What payload do I want to lift?”

The wing does not care how you divide up weight. If you build a 10,000lb airplane that’s creating 500lbs of drag at high altitude, you’ve got a 20:1 L/D ratio. That’s an excellent ratio, BUT…what are you lifting? If your aircraft empty weighs 7,000lbs and your useful load is 3,000lbs, it means you are experiencing a 6:1 load to drag ratio. If on the other hand your aircraft weighs 5,000lbs empty and your load is also 5,000lbs, your load to drag ratio goes up to 10:1 (designer Barnaby Wainfan describes this as an aircraft’s “transport efficiency” in his excellent article on low aspect ratio wings in the February 1997 issue of Flight Journal). Losing a bit of total L/D may be worth it to increase load to drag. Thus begins the tradeoff between light structure and increased L/D. Longer wings are heavier wings, with the attendant bending moments, possible zero-fuel restrictions and clearance problems for taxiways and hangars.

Yes, this high aspect ratio glider is efficient, but only at low relative speeds.

Yes, this high aspect ratio glider is efficient, but only at low relative speeds.

The other missing aspect is airspeed. While discussing the D-21 triple-sonic drone in his book “Aurora”, Bill Sweetman calls attention to its relative efficiency compared with a B-52. Using a modified version of the Breguet Range Equation, he multiplies the L/D of each aircraft by its cruise Mach. The B-52 with a 19:1 L/D and a Mach 0.85 cruise came out at 16:1. The D-21 with a 6:1 L/D and Mach 3.5 comes out to 21:1.

While this number (Mach to drag?) doesn’t do much since it ignores the D-21’s limited fuel supply compared with the B-52’s massive reserves and therefore does not give any useful information on actual range, it is interesting nonetheless. Personally, I’d use it as an early benchmark in the design process. If your intent is to go fast, a lower L/D is not as damning as one might expect, particularly since you’re “wasting” fuel for a shorter interval of time to cover a similar distance as a slower aircraft. This of course assumes you are not travelling supersonic where thrust specific fuel consumption begins to rise, further eating away at your endurance (but if your drag is low enough, you may still be able to recover range by the increase in speed…whew!). One way or the other, you’re putting either the slow penny or the fast nickel out your exhaust pipe.

I tried and probably failed miserably to get the point across. The point being that L/D is just one part of the equation when it comes to efficient design. If I had a choice between an airplane that had an L/D of 8:1 and a load to drag of 14:1 versus an airplane with an L/D of 18:1 and a load to drag of 5:1, I’d pick the 8:1 L/D aircraft 50% of the time…maybe.

Why? Because what I intend to do with the aircraft is what should drive its design. I’m not going to lie and say that high aspect ratio or low aspect ratio is better than the other because they’re not. I’m not going to say ignore L/D completely because that’s just stupid. But I do recommend that you look at your range, speed and payload requirements before committing to a design. Simply copying what comes out of Renton or Wichita doesn’t make much sense if you’re going to be doing something different than what they intended with their designs.

In summary, what did we learn?

  • Low aspect ratio aircraft tend to have lower empty weights and can be very strong structurally.
  • High aspect ratio aircraft tend to have higher empty weights and can require extra strengthening in extreme cases.
  • Lift to drag ratios are not fully useable until you know what fraction of the weight is payload/useful load.
  • An airplane with a high L/D and high aircraft empty weight has less transport efficiency (thanks Mr. Wainfan!) than an airplane with a lower L/D and lower empty weight.

Unfortunately, like most things in aviation, what I brought up here leaves a lot more to be addressed, like the role of wing loading, or integration of wings and fuselages. Or even why all my designs look like guitar picks (seriously, not all of them). We’ll continue soon with more on wing loading and how reducing it can improve high speed performance.

Dyke Delta N18DW at Oshkosh. Low aspect ratio double delta wing design very resistant to stalls and adds at least 200mph to every pass, at least in the spectator's mind.

Dyke Delta N18DW at Oshkosh. Low aspect ratio double delta wing design very resistant to stalls and adds at least 200mph to every pass, at least in the spectator’s mind.