NEUTRAL STABILITY - German V-2 Example

[Ez2cDave]

I believe that the Early versions of the German V-2 rocket suffered from "Neutral Stability", which corrected itself, after sufficient fuel was burned to move the CG forward . . .

The problem was corrected, in later flights.

This video shows the basis for my hypothesis :



Dave F.

 

[SolarYellow]

Or they might have gotten the analog electronic guidance system tune dialed in better.

 

[Antares JS]

If the V-2 only had passive guidance, you might be right, but the fact that it had active guidance makes that hypothesis questionable at best.

 

[smstachwick]

Looks like rod whip to me

 

[Ez2cDave]

Or they might have gotten the analog electronic guidance system tune dialed in better.

True, but the rocket was "squirrely" from first motion, before sufficient airspeed for the fins to become effective.

Also, the first rockets attained stability, later in the flight . . . I surmise that it was after the CG moved forward, due to fuel consumption.

 

[Art Upton]

True, but the rocket was "squirrely" from first motion, before sufficient airspeed for the fins to become effective.

Also, the first rockets attained stability, later in the flight . . . I surmise that it was after the CG moved forward, due to fuel consumption.

Real guidance was not the Fins but the graphite Vanes in the exhaust with the V2?

 

[Art Upton]

ALSO CG with fuel full forward would move backwards as the fuel was consumed ??

DAVE, DAVE?? "Dave is not here' ... No I AM DAVE.. "No Dave is not here" ...

 

[Ez2cDave]

ALSO CG with fuel full forward would move backwards as the fuel was consumed ??

DAVE, DAVE?? "Dave is not here' ... No I AM DAVE.. "No Dave is not here" ...

I never said the CG moved backwards . . .

The WARHEAD ( 2,150 lb ) was in the Nose Cone . . . So, the CG would move forward, as fuel is consumed.

Otherwise, the rocket would become progressively more unstable, if the CG moved aft during flight.

Dave F.

 

[OverTheTop]

The WARHEAD ( 2,150 lb ) was in the Nose Cone . . . So, the CG would move forward, as fuel is consumed.

Careful how you think about this. In a solid motor the mass at the rear of the rocket gets lighter as we burn it, moving the CG forward. In liquid/hybrid rockets the remaining fuel is at the rear of the rocket, with the empty ullage at the front of the tanks increasing in size. The CG of the fuel actually shifts aft, taking the remaining CG of the rocket partly aft with it. The heavy warhead somewhat mitigates this effect.

Incidentally, there used to be a question on this in the L2 exam for Tripoli.

 

[Ez2cDave]

Careful how you think about this. In a solid motor the mass at the rear of the rocket gets lighter as we burn it, moving the CG forward. In liquid/hybrid rockets the remaining fuel is at the rear of the rocket, with the empty ullage at the front of the tanks increasing in size. The CG of the fuel actually shifts aft, taking the remaining CG of the rocket partly aft with it. The heavy warhead somewhat mitigates this effect.

Incidentally, there used to be a question on this in the L2 exam for Tripoli.

Difficult to determine, without knowing the launch CG of an actual V-2 rocket . . . Also, where is the CP located, on a real V-2 ?

Yes, that question dealt, primarily, with Hybrid-powered rockets.

Dave F.

 

[Sooner Boomer]

Careful how you think about this. In a solid motor the mass at the rear of the rocket gets lighter as we burn it, moving the CG forward. In liquid/hybrid rockets the remaining fuel is at the rear of the rocket, with the empty ullage at the front of the tanks increasing in size. The CG of the fuel actually shifts aft, taking the remaining CG of the rocket partly aft with it. The heavy warhead somewhat mitigates this effect.

Incidentally, there used to be a question on this in the L2 exam for Tripoli.

I disagree. At launch, the fuel/oxidizer tanks in the rear are full, biasing the CG towards the rear. As the propellants are burned up, the mass at the rear is less, making the rear weigh less. If the rear (aft) weighs less, the balance point, the CG, is moved forward.
[edit] I re-read your comment - you state that the CG of the *fuel* moves aft. Indeed it does. The CG of the entire rocket, however, moves forward.

This has an interesting effect with active guidance. If the CG is much ahead of the CP, the rocket is stable. If lateral forces act to disturb direction of flight, the CG/CP relationship acts to bring the rocket into line. If the CG is *at* the CP, the rocket is neutrally stable. Lateral forces can easily perturb the direction of flight. With neutral stability, fins/exhaust vanes can more easily steer the rocket than if it were stable. Taking this a step further; if the CG is *aft* of the CP, the rocket is unstable (or negatively stable). The rocket does not want to fly straight. Lateral forces can easily cause the flight path to deviate. If you have active guidance, for example in an air-to-air or ground-to-air intercepter missile, haveng neutral or even negative stability makes the rocket agile and very easy to change direction.

 

[OverTheTop]

I disagree. At launch, the fuel/oxidizer tanks in the rear are full, biasing the CG towards the rear. As the propellants are burned up, the mass at the rear is less, making the rear weigh less. If the rear (aft) weighs less, the balance point, the CG, is moved forward.
[edit] I re-read your comment - you state that the CG of the *fuel* moves aft. Indeed it does. The CG of the entire rocket, however, moves forward.

If you think of the weight of the fuel being a lumped mass (good assumption) then the CG of the fuel actually moves aft, even though the total mass reduces. The same applies to the oxidiser. CG of oxidiser moves aft even as the mass of oxidiser is reducing. How it moves the overall CG depends on the structure of the A4.

Let's put some bones on this:


I am going to make a guess that the CG of the dry rocket is towards the front of the LOx tank.
As the oxidiser is consumed the CG of the oxidiser will move aft, moving the CG of the rocket aft.
As the alcohol is consumed the CG of the alcohol will move aft, moving the CG of the rocket aft.

So as the rocket flies the CG moves aft, and then at some point the dry mass CG will start to win and pull the CG back towards the front since the mass of the liquids is becoming smaller and less relevant. Dry mass is around 12.5 tonnes, making the liquids (nearly 9 tonnes) more than 72 percent of the mass. Shifting CG of the liquids will have a significant effect on CG position, first dragging it aft, then allowing it to move back forward as the fuel/oxidiser runs out.

Think about it. Consider the CG of each liquid as the flight progresses.

 

[Sooner Boomer]

"Think about it. Consider the CG of each liquid as the flight progresses."

from Wikipedia:
fuel mass - 3.810kg
LOX mass - 4,910
Warhead mass - 1,000kg

I don't know the mass of the engine, turbopump, or fins.

From studying the masses involved, and their respective locations, I think you're right. I didn't realize how much mass there was in the aft of the rocket.

 

[Ez2cDave]

"Think about it. Consider the CG of each liquid as the flight progresses."

from Wikipedia:
fuel mass - 3.810kg
LOX mass - 4,910
Warhead mass - 1,000kg

I don't know the mass of the engine, turbopump, or fins.

From studying the masses involved, and their respective locations, I think you're right. I didn't realize how much mass there was in the aft of the rocket.

https://www.thisdayinaviation.com/tag/v2/

EXCERPT :

"The V2, or Vergeltungswaffen 2 (also known as the A4, or Aggregat 4) was a ballistic missile with an empty weight of approximately 10,000 pounds (4,536 kilograms) and weighing 28,000 pounds (12,700 kilograms), fully loaded. It carried a 738 kilogram (1,627 pound) (sources vary) explosive warhead of amatol, a mixture of TNT and ammonium nitrate. The propellant was a 75/25 mixture of of ethanol and water with liquid oxygen as an oxidizer."

END EXCERPT :

This gives us a "dry weight" for the rocket of 10,000 lbs. +/- ( 4,536 kg ).

ALSO, it is interesting to note the Warhead weight of 1,627 lb ( 738 kg ) . . . This data appears to be for the early V-2 rocket, since later versions are documented as having a Warhead weight of 2,150 lb ( 975 kg ) . . . An increase of 523 lb. ( perhaps to achieve a more forward CG, by adding more explosives, as opposed to "dead weight" ballast ).

https://en.wikipedia.org/wiki/V-2_rocket

EXCERPT :

"The warhead was another source of trouble. The explosive used was amatol 60/40 detonated by an electric contact fuze. Amatol had the advantage of stability, and the warhead was protected by a thick layer of glass wool, but even so it could still explode during the re-entry phase. The warhead weighed 975 kilograms (2,150 lb) and contained 910 kilograms (2,010 lb) of explosive. The warhead's percentage by weight that was explosive was 93%, a very great percentage when compared with other types of munition.

END EXCERPT :

I believe that the Warhead weight was increased to move the CG forward.

Dave F.

 

[Ez2cDave]

Some interesting data on the V-2 . . .

Dave F.

 

[bjphoenix]

I would guess that the CG of the rocket is relatively close to the center, (unless the motor and pumps are really heavy) and those fins are fairly large, so it is very surprising that it would not be stable at launch.
I remember the original Estes V2 (BT55) required a bit of nose weight if it was built with scale fin dimensions. I built a larger version based on the Estes Silver Comet, with 24mm mount and dimensions from Peter Alway's book. It is plenty stable even if it's mostly hollow except for the D12 at the back end. The real V2 looks like it is pretty much completely full of stuff which is why I thought the CG would be fairly far forward.

 

[aerostadt]

In general liquid oxygen is denser than ethyl alcohol, so the German engineers might have gained a little more stability putting the liquid oxygen tank ahead of the ethanol tank. However, there was an advantage for routing the alcohol through a pipe line through the LOX tank. This cooled the alcohol and helped with the regenerative cooling. Note that in the Space Shuttle ET the LOX tank is ahead of the liquid hydrogen tank. Of course, the Shuttle had vectored nozzles for the SRB's and the Orbiter, but I am wondering if putting the LOX tank forward help promoted stability.

Note that the V-2 had graphite vanes in the exhaust, but I believe there were also small vanes on the fins. Of course, when the V-2 got out of the lower atmosphere the fin vanes were no longer effective. Likewise, the graphite vanes were only effective as long as the motor was burning.

 

[Daddyisabar]

Looks like rod whip to me

In my best Peter Seller's accent: "Mein Fuhrer, it vas die rod's fault!"