optimum altitude

Norris states, according to the AOPA article, that the most efficient way to use any aeroplane is to fly it at a speed equal to 1.31*Vy

The altitude that gives you 1.3 times Vy at full throttle and at your cruise RPM and while leaned out is your "optimum" altitude for a normally aspirated engine.

Does this also apply the same for a turbocharged aeroplane?

Or what is the "optimum" altitude for a turbocharged aeroplane?

I would think so, yes. Your "optimum" altitude in the turbo's case would be whatever altitude above critical that your MP came down to the point where you attained your 1.3 x Vy. Maximizing true airspeed (TAS) while minimizing burn rate.

Some turbo'ed aircraft wouldn't allow for it though. A Malibu's service ceiling is 25K and its critical altitude is the same. When set up right mechanically the engine will maintain its full 42 inches all the way up. Not that it couldn't go higher, but the ceiling was set at 25K to keep pilots from needing a high altitude sign off to fly it. Seneca V's are the same way. Critical altitudes for something like a Turbo Bonaza, Saratoga TC, T-206 are in the mid teens... the formula could be applied in their cases. You would be on the bottle though and in the TC's case somewhere 'tween 18 and 20K.

But in the Malibu's case or similar I would say that its optimum altitude is the one in which you maximize TAS while maintaing normal economy cruise settings. Only limiting factor on the airplane's part could be temp limits when operating that high. I often have to pull it back a couple inches and/or increase fuel flow when up high to keep from cooking the cylinders depending on ambient conditions. Mileage can vary from aircraft to aircraft.

When calculating optimum, don't forget that speeds change with weight, as do climbs...

Optimum also has to do with distance traveled for time in climb....

I think that is why I like 5 miniute flights at 200'; no thought 8)

I think it's actually 1.316 * L/D Max(best glide), not Vy. They are close, but different. Google "Carson Speed", "Carson Cruise" or "CAFE" for a more complete explanation. Carson, a Naval Aviator, crunched the numbers and came up with this formula.However, all things considered, in the end, picking the altitude with the most favorable winds will usually have the biggest effect on efficiency with propeller driven aircraft.

Here's a link to another perspective.

http://www.flyingmag.com/technicalities/755/the-very-best-speed-to-fly.html

Ummm, WSH, any idea where there's a published L/D polar curve, especially with L/D Max, like a Dick Johnson test? I'll bet Dick's brother Dave had a pretty good idea what that number was.

Thanks. cubscout

Cubscout

No, I don't. I've been looking for one for the 12 and have been to lazy to make one up on my own.

'Nother fly in this ointment. My normal "milk run" in the C182 is VA-FL and back, a 1400nm round trip. Right out of the Owners Manual, go fast mode at 10,000' is 19"/2450 for 134 ktas and 12 gph. Economy is 19"/2000 for 113 ktas and 9gph. So we have a 3 gph differential between wide open and economy. Going fast for the round trip takes 10+26 and 125 gals. Economy takes 12+23 and 111 gals. So, slower saves me about 14 gallons for the round trip or about $56 at $4 a gallon. OTOH, it cost me nearly 2 extra hours of my time and worse than that, nearly 2 hours more on the engine and aircraft. And for the C182 at a cost of about $120 an hour dry for everything,insurance,hangar,maintenance,engine fund,loss of cash capital,ect.,ect,...

So, to that end, it's costing me (around) $180 MORE to go slower and get there two hours later!:lol: Doesn't get much better than that!

John Anderson's Introduction to Flight has the equations for Range and Endurance, both for reciprocating propeller engines, and turbo jets/fans.

For a normally aspirated piston prop the Breguet formula shows range is maximised with (i) highest propeller efficiency (ii) lowest SFC (iii) maximum L/D (not 1.32Vy which is Mmr for jets) and highest ratio of fuel weight. This speed for L/D max is the tangent to the Power required curve and approximately Vy. In a piston prop, no wind condition, maximum range is independent of altitude, although rho is a factor for maximum endurance.

To achieve lowest SFC jets like cold air, and the calculus uses the Thrust required curve, hence the tangent being 1.32Vy. This speed is where (CL square root)/Cd is maximum, or where zero lift drag is three times lift dependant drag. SFC improves massively the lower the turbine inlet temperature, and rho or density figures in the Jet Breguet formula as inversely proportional to Range. In theory if the wing could fly and not encounter transonic drag, or low speed buffet, the highest possible altitude is optimum in a jet.

The maths is quite elegant, but cutting through it, it is nice to see that a Super Cub optimum altitude for either range or endurance is MSA, or away from built up areas and TV masts, around 500 feet AGL.

In the 95 HP SC this equates to 45-50% economy cruise at around 75-80mph. This assumes propeller efficiency for the fixed pitch prop is close to optimum at around 75-85 mph. Arguably 80-85 mph is more speed stable (L/D Max is speed neutral), and smooth air altitude (assuming no wind) would be ideal. Climbing to full throttle altitude at this IAS might improve SFC slightly but not to overcome the fuel used to climb. The L18C has 35 usg capacity, so at 45-50% power this is close to 9 hours with VFR reserves, or around 700 sm.