Fuel efficiency nomogram (kilometerförbrukning)

[Pyrocumulous]

For the below kilometerförbrukning nomogram, how do I calculate the percent fuel per kilometer? I've drawn (red) 0.55 mach, turned right (purple) at 1600kg flight weight (flygvikt). Where do I turn up on the DELTAD quadrant?
I assume that this is a point in time, so if for a flight segment I start at 19000kg and end at 13000kg, 16000kg would be a decent approximation of the average flight weight. Is this correct?
Testing the above approximation for a full 127.5% fuel cycle (rather than just a snapshot in time, since I don't have a way to precisely measure fuel in the tanks), I flew 1075km at ISA-15 and 5m altitude for approximately 0.12 percent per kilometer.

[buur]

hard to say, your scan is a little bit small so I cant read the numbers. Have you a link to the original source?

But looking on the example given in the diagram, you have to follow the first inclined line you purple line hits up to the DELTAD value.

[Pyrocumulous]

The example line looks like it would make sense if I knew what DELTAD was referring to. My assumption is that it a drag coefficient.
That is from page 93 of this document:
https://www.ftfsweden.se/wp-content/uploads/2016/11/Fpl-AJ-37-speciell-förarinstruktion-SFI-del-3.pdf
 

Edited December 27, 2024 by Pyrocumulous
correct page number

[Pyrocumulous]

I found it in the lastalternativtabell (load option table?) on Page 8 of that document. It appears that you just look up the at start, 100%, 70%, and 40% fuel and then you have weight and the resistance (DELTAD) at several reference machs. It looks like jettisoning the external tank results in a -5 DELTAD.

[buur]

DELTAD as drag coefficient make sense. And also the posted table gives you the right information.

[Pyrocumulous]

Here is an example for a jet fully fueled with external tank (XT) and four racks of bombs (SB) at sea level and 0.55m.
It's curious that according to the nomogram, 0.50m should be the most efficient mach at sea level for all loads, but the Heatblur manual indicates 0.55m.

Edited December 27, 2024 by Pyrocumulous
add observation about 0.50m

[Machalot]

On 12/27/2024 at 1:27 PM, Pyrocumulous said:

It's curious that according to the nomogram, 0.50m should be the most efficient mach at sea level for all loads, but the Heatblur manual indicates 0.55m.

I read it the same way until I realized you can't just compare curves on the right plot, you have to start from the beginning.  Mach 0.5 is not actually more efficient because you start much higher on the lefthand plot.

Edited January 2 by Machalot

[HILOK]

hi and happy new year !
just out of curiosity, what would "B/V %Km" mean ?

[TOViper]

Happy new year guys!

Interesting discussion here.
I read the left diagram as the lift-induced drag of the aircraft, and the middle table as the form/interference drag penalty of external stores.
Does anybody know if this very diagram was implemented in the code, maybe @MYSE1234?

Just did a quick flight:
It's amazing to see the Viggen flying in zero meters with 100% fuel for 1200km at Mach 0.85 (clean) @ISA.
The "B/V %KM" value would be ~0.104 at 15.2 tons , and ~0.1025 at 10.7 tons.
So the min/max distances would be 100/0.104 = 961km and 100/0.1025 = 975 km, so I guess the diagram is not implemented right now.

Never mind, the Viggen is great.

Edited January 2 by TOViper

[Pyrocumulous]

16 hours ago, HILOK said:

hi and happy new year !
just out of curiosity, what would "B/V %Km" mean ?

I believe:

• B = bränsle = fuel
• V = väglängd = distance

It appears essentially to be percent fuel per kilometer. Think of it as kilometers per liter (but the inverse, so lower number is more efficient), but we don't have a fuel gauge that measures in liters or kilograms, so they used percent capacity of the fuel tank. Each percent of the fuel capacity is about 42kg of fuel.

Edited January 3 by Pyrocumulous
clarification

[HILOK]

12 hours ago, Pyrocumulous said:

I believe:

• B = bränsle = fuel
• V = väglängd = distance

It appears essentially to be percent fuel per kilometer. Think of it as kilometers per liter (but the inverse, so lower number is more efficient), but we don't have a fuel gauge that measures in liters or kilograms, so they used percent capacity of the fuel tank. Each percent of the fuel capacity is about 42kg of fuel.

thanks. hmm interesting, i wonder how the wind effect is accounted for? but maybe wind is not really relevant in case of the viggen's flight profile? -i assume relative short distances low-level flying?

[renhanxue]

On 1/2/2025 at 8:33 PM, Pyrocumulous said:

I believe:

• B = bränsle = fuel
• V = väglängd = distance

It appears essentially to be percent fuel per kilometer. Think of it as kilometers per liter (but the inverse, so lower number is more efficient), but we don't have a fuel gauge that measures in liters or kilograms, so they used percent capacity of the fuel tank. Each percent of the fuel capacity is about 42kg of fuel.

B for bränsle is a reasonable guess but "väglängd" is not really a word that a native Swedish speaker would ever use. The word used for distance would be "flygsträcka" (distance flown), as seen in the headline above the diagram.

Percentage points fuel used per kilometer flown is indeed the correct interpretation of the number, but what "B/V" actually stands for I don't know. Note the percentage points though.

12 hours ago, HILOK said:

i wonder how the wind effect is accounted for?

It's not accounted for at all in this diagram, since it's not really relevant. The diagram gives you the fuel consumption at a given Mach, that is indicated airspeed, that is relative to the atmosphere, so wind doesn't change any of the numbers. All it does is just make you go slower or faster over the ground, so it's straightforward to just calculate how much longer you have to fly through the air to get where you want.

On 1/2/2025 at 11:18 AM, TOViper said:

So the min/max distances would be 100/0.104 = 961km and 100/0.1025 = 975 km, so I guess the diagram is not implemented right now.

Did you try with the drop tank? The value should be interpreted as "indicated percentage points", so with the drop tank you start at ~127% or something like that. Also note the diagram is static; as you burn fuel the aircraft gets lighter and the drag is continuously reduced over the course of the flight.

Edited January 3 by renhanxue

[renhanxue]

Here's the original full resolution JPEG that I used to make the "scan" by the way, just in case it helps anyone (link to maybe make it easier to view it in full resolution). As you can see the example line was red in the original.

Edited January 3 by renhanxue

[Machalot]

On 1/2/2025 at 2:18 AM, TOViper said:

Does anybody know if this very diagram was implemented in the code, maybe @MYSE1234?

Similar to diagrams of instantaneous and sustained turn performance, climb performance, acceleration, etc., this diagram is not directly "implementable" per se because it doesn't represent a general model of the flight dynamics.  Rather it is calculated from the combination of the underlying flight dynamics models (propulsion, mass, atmosphere, and aerodynamics), under a set of very narrow assumptions, e.g. trimmed steady level flight with a specific mass center.  Each of those models accepts flight condition and aircraft state (e.g. fuel, payload, power setting) as inputs, and provides a set of outputs (e.g. angle of attack for steady level flight, drag, thrust, fuel flow rate, control deflections for trim, etc.) and those outputs are then combined in another set equations to produce a diagram like this.

If those other models and assumptions are implemented accurately, any point on this diagram should be reproducible.

Edited January 7 by Machalot