× Welcome to the CPL Aerodynamics question and answer forum. Please feel free to post your questions but more importantly also suggest answers for your forum colleagues. Bob himself or one of the other tutors will get to your question as soon as we can.

## Glide Range and Endurance

• Mutley Eugenius

### Mutley Eugenius replied the topic: Range and Endurance

Bob you have given great explanations here, but I haven't seen anyone ask this question yet...

Best glide (lift/drag) ratio as you have described first up is at about 4 deg AoA. And a heavier plane will do this at a faster airspeed.

SO, if a fully loaded 172 next to an almost completely empty (1 pilot no fuel) 172 in side-by-side formation both pulled their power all off at the same time and settled on a 4 deg AoA, they could both be expected to follow the same glide path, with the heavier plane gliding at a faster speed, and arrive at the same ground point dead ahead, with the heavier plane getting there first. OK, cool.

BUT in the 172 POH it says that best glide is 64 KIAS. Or 65, depending on who you ask. Whatever.

Thus, the KIAS airspeeds of these two planes are going to be different, right? I mean how can both the heavier and the slower plane both be achieving the advertised best glide at 64 KIAS?

AND, that being asked, what if they DID both attain 64 KIAS? Would the heavier plane then have a greater descent rate and then thus a shorter glide range?

This is an experiment that I would absolutely LOVE to do one day with two planes in the training area, and then video it, just to publish the physical results for the student pilot world to watch.

• Posts: 2449

### bobtait replied the topic: Range and Endurance

Lift and drag result from the behaviour of the passing airflow as it interacts with the SHAPE of the aircraft. The WEIGHT of the aircraft has nothing to do with it. Here is a 'thought experiment'.

Imagine we have an actual Cessna 152 and an exact replica that has been carved out of solid lead. Now we place them in a wind tunnel with each at the same angle of attack and the same airspeed. The air flowing around the two would produce exactly the same amount of lift and drag and therefore the same lift/drag ratio because their SHAPES are identical. Their vastly different weights would have nothing to do with that.

The actual amount of lift and drag generated by each of these imaginary aircraft would depend upon the angle of attack and indicated air speed and nothing else.

However, if we expected the solid lead 152 to actually fly at that angle of attack, it would have to fly at a ridiculously high speed (so much for that idea!). The lift/drag ratio is also the distance/height ratio (see page 93 of the Aerodynamics book. Fig 8.14). There is only one angle of attack that will produce the best lift/drag ratio and, provided you fly at that angle of attack, you will achieve the best gliding distance in no wind.

Theoretically, every weight would have its own gliding speed for the best lift/drag ratio. However, for the average GA type aircraft, the difference between very empty and very full would be so small as to be safely ignored. To conduct the in-flight experiment you have suggested, you would actually need an angle of attack meter in the cockpit. The heavier aeroplane would have a higher rate of descent, but that is because it comes down the same slope faster.
The following user(s) said Thank You: Mzahr

• Mutley Eugenius

### Mutley Eugenius replied the topic: Range and Endurance

Thanks Bob,

That's a fascinating example! I'm intrigued then to see you write that the difference between full and empty is ignorable. And I'm still a bit hazy on it. For a Cessna 172 with a wing surface area of 16.2 square metres, a single pilot empty weight (720 Kg) gives about 44 Kg per square metre, but a full weight (1100 Kg) spreads 68 Kg per SqM. That means empty weight is only 2 thirds of full weight.

So are you saying that this 50% increase in empty weight to full weight causes a speed increase down this best glide angle of attack that is negligible compared to the recommended 65 KIAS?

That's hard to imagine, considering your solid lead Cessna approaching supersonic to get the required lift. Makes me want to try that too!

• John.Heddles
• Offline
• ATPL/consulting aero engineer
• Posts: 853

### John.Heddles replied the topic: Range and Endurance

I don't have your particular POH page to review. Perhaps you might post a photo of it ?

I expect that it will indicate that the speed recommended is for a specific (probably gross) weight. I checked the C172N POH and the speed nominated is for MTOW, for example.

Engineering specialist in aircraft performance and weight control.

• Mutley Eugenius

### Mutley Eugenius replied the topic: Range and Endurance

Thanks both very much to you both, I went hunting and found this on 'Bold Method":

"There's something you need to keep in mind about best glide, though. Like most airspeeds in the POH, best glide is calculated at max gross weight. And as weight decreases, so does the speed that will maximize your distance. The change is minor, but if you're trying to get the most out of your glide and you're lighter than max gross weight, a slightly slower speed may help you out."

www.boldmethod.com/learn-to-fly/maneuver...m-sink-how-to-do-it/

• John.Heddles
• Offline
• ATPL/consulting aero engineer
• Posts: 853

### John.Heddles replied the topic: Glide Range and Endurance

I notice a lot of references just sort of say to reduce speed a little if weight is less than MTOW.

With the L/D constrained, the sums become reasonably straightforward. You have chosen not to give us your specific model so I'll work on the 172N I downloaded before. Using the standard sums, I get figures along the lines of

2300 lb 65 KIAS (quoted in the POH)
2000 lb 61 KIAS
1800 lb 55 KIAS

I haven't plotted the PEC so the figures might be out a knot compared to a more accurate calculation.

Engineering specialist in aircraft performance and weight control.

• Mutley Eugenius

### Mutley Eugenius replied the topic: Glide Range and Endurance

Thanks for that John. What calculation are you using to figure it out?

And it's not that I chose not to give you my specific model, but there are about 25 different Cessna aircraft in my logbook, so I didn't know which one to pick.

• John.Heddles
• Offline
• ATPL/consulting aero engineer
• Posts: 853

### John.Heddles replied the topic: Glide Range and Endurance

What calculation are you using

We have constrained L/D, which constrains alpha and CL. If we equate CL for two weight cases, we end up with

Vc2/Vc1 = √(W2/W1)

where Vc1 is CAS and W1 is weight for case 1.

Engineering specialist in aircraft performance and weight control.

• Posts: 6

### Mzahr replied the topic: Range and Endurance

BOB TAIT

Hi Bob, Amazing explanation ! Would just like to confirm my thoughts regarding the best L/D ratio Glide speed understood when weight changes speed changes for obvious reasons to achieve same AOA lighter A/C requires lower speed to increase its AOA required to achieve the Best L/D ratio , as you have explained that theoretically each speed below the known max weight speed that gives you the required AOA at max speed subsequently all other weights below this weight will require their own Glide speed , Now my question is the faster A/C at the BEST L/D AOA gliding down the same path ( same as shooting a 3 degree Glide slope, faster GS means Higher descent rate , slower aircraft slower decent rate but both will remain on the 3 degree Glidepath understand this regarding the GLIDE ANGLE , but doesn’t this mean that the faster aircraft now has more parasite drag than the slower aircraft therefore reducing its range capabilities ? Compared to the slower aircraft this is my confusion how I answer this is the heavier A/C the drag is proportional to the square of the aircraft , and the lift prop to the speed because of heavier weight this means the Drag associated from the speed is balanced by the additional thrust that is achieved by the extra weight of the A/C from gravity ? am i on the right concept here about the extra weight creating extra speed therefore extra drag but this is cancelled out by the additional speed so it doesn’t affect its range ? Hope I have explained best I can but this is where I have Dug my hole trying to work out why still get the same range with faster speed and heavier understand everything regarding rate of decent / faster speed / best lift drag AoA . But it’s just how the extra parasite drag from faster A/c doesn’t affect the glide distance /range.

• John.Heddles
• Offline
• ATPL/consulting aero engineer
• Posts: 853