Particularly minute minutiae of nosecones in stock aerodynamics

[OhioBob]

Losses are expressed in delta-v. Velocity is a function of acceleration, v = at. Acceleration is a function of force and mass, F = ma. In stock KSP drag is proportional to the product of mass and drag coefficient, F ∠mC_d.

F = ma ---> a = F/m

F ∠mC_d. ---> F/m ∠C_d

Therefore, by substitution

a ∠C_d

Likewise,

v ∠C_d

When the drag coefficient decreases, the resulting velocity loss also decreases.

It's true that adding a part increases the drag force, but that drag force is trying to slow down a more massive object. When you add a part that does not change the drag coefficient, the drag force and the mass both increase by an equal fraction. The acceleration produced by the drag force does not change and, hence, the drag loss does not change. However, when you add a part that decreases the drag coefficient, the drag force increases proportionally less than the mass increases. We have,

F₁ ∠m₁C_d1 ---> F₁/m₁ ∠C_d1

F₂ ∠m₂C_d2 ---> F₂/m₂ ∠C_d2

If C_d2 < C_d1, then F₂/m₂ < F₁/m₁.

F/m is, or course, acceleration. If the acceleration is lower than clearly so is the resulting velocity. In this case the velocity is negative and is the drag loss.

Edited December 14, 2014 by OhioBob

[Starman4308]

If you add a low- drag part to an assembly in KSP, you have still added drag. It does not matter that it's less drag than what would've been added with a normal part, it is still more drag than you had without it.

And that's really all that matters. You cannot add drag and then expect lower losses from it. It simply doesn't work that way, at least not in stock soupodynamics.

If you add drag, you increase losses from drag.

It's not a contradiction. Let's take an illustrative example with a similar property: ascent from an airless planet with variable Isp.

Assume for a moment that we have two mostly-identical rockets. Rocket A has a 400s engine, while Rocket B has a hole in a fuel line, and only gets 200s Isp. At the moment of launch, both perform identically, except with Rocket B using twice as much fuel. As time goes on, however, Rocket B uses up more of its fuel, and can go horizontal more quickly, because it no longer has to spend as much thrust fighting gravity. Rocket A, burdened by unspent fuel, falls increasingly behind, and must use more acceleration fighting gravity.

When you add things up in the end, Rocket B spent less delta-V fighting gravity. However, Rocket A has used less fuel, because it had the more efficient engine. If you define "gravity drag" as being in delta-V terms, Rocket B is the winner, but if you care about the overall result, Rocket A spent much less fuel.

This is what is going on with stock nosecones. You lose less delta-V to atmospheric drag, because your average Cd was lower and terminal velocity was higher. However, by having the nosecone, you reduced the overall delta-V and TWR available, and as such, you get to orbit with less fuel and less delta-V.

EDIT: In short, your gut instinct is correct: stock nosecones are a bad thing. They only seem to be a good thing because of a giant loophole in how atmospheric drag is defined, as a loss of velocity. It'd be a bit like minimizing gravity drag by going with a 4.0 TWR rocket: it's not actually helping the overall problem (getting to space with the most payload), it's just making one component of the problem look less bad.

Edited December 14, 2014 by Starman4308

[OhioBob]

Really bad analogy:

Let's try this one. Say we have a truck traveling down the road and we throw it into neutral and let the it coast to a stop. (Let's ignore rolling resistance say it is only drag that slows it down.)

We now fill the bed with a load of stone. Let's say the aerodynamics of the air flow around the load increases the drag 10%. However, the weight of the load increases the total mass of the vehicle by 30%. If we now repeat the previous test and throw the truck into neutral on the same road at the same initial speed, what will happen? The truck will decelerate more slowly and travel further before coming to a stop. This is because we have 1.1 times as much force trying to slow down 1.3 times as much mass. The loaded truck, with more mass behind it, will cut trough the air more easily.

[arkie87]

Let's try this one. Say we have a truck traveling down the road and we throw it into neutral and let the it coast to a stop. (Let's ignore rolling resistance say it is only drag that slows it down.)

We now fill the bed with a load of stone. Let's say the aerodynamics of the air flow around the load increases the drag 10%. However, the weight of the load increases the total mass of the vehicle by 30%. If we now repeat the previous test and throw the truck into neutral on the same road at the same initial speed, what will happen? The truck will decelerate more slowly and travel further before coming to a stop. This is because we have 1.1 times as much force trying to slow down 1.3 times as much mass. The loaded truck, with more mass behind it, will cut trough the air more easily.

I am a bit confused. Are you and GoSlash27 talking about stock aerodynamics or FAR?

With FAR, the loaded truck will go farther (as it will in real life) since it has more momentum at the same speed (i.e. more mass) so it will take a longer distance to stop it, despite it having a nominally larger drag.

With stock, the empty truck will go farther because adding high drag parts increases total (and average) drag. Mass is not a factor since drag force is (incorrectly) proportional to mass always.

Edited December 14, 2014 by arkie87

[Starman4308]

I am a bit confused. Are you and GoSlash27 talking about stock aerodynamics or FAR?

Stock aero. FAR has never entered this conversation, because we all know nosecones are a good idea with FAR.

With stock, the empty truck and the truck full of generic rocket parts go the exact same distance, because both of them have the same inertia/drag ratio. However, the truck full of nosecones goes farther, because nosecones only have drag proportional to 0.1*mass, instead of 0.2*mass: thus, the truck has an overall lesser drag coefficient, and thus has more inertia/drag.

[arkie87]

Stock aero. FAR has never entered this conversation, because we all know nosecones are a good idea with FAR.

With stock, the empty truck and the truck full of generic rocket parts go the exact same distance, because both of them have the same inertia/drag ratio. However, the truck full of nosecones goes farther, because nosecones only have drag proportional to 0.1*mass, instead of 0.2*mass: thus, the truck has an overall lesser drag coefficient, and thus has more inertia/drag.

Sorry. Title says "FAR and Stock"

[OhioBob]

Mass is not a factor since drag force is (incorrectly) proportional to mass always.

Incorrect. Drag force is proportional to mass x drag coefficient. If mass goes up while the drag coefficient goes down, then both quantities go up but not by the same proportion. In stock the difference is very small but it is there.

With stock, the empty truck will go farther because adding high drag parts increases total (and average) drag.

That is the misconception that I've been arguing against. It is not the magnitude of the drag force that determines how fast the vehicle slows down - it is the acceleration that the drag force produces, i.e. a = F/m. While adding parts increases the drag, it also increases the mass. Both together must be taken into consideration. It is not valid to make the blanket statement that increasing drag force increases drag losses. Drag force and drag loss are not the same thing.

[OhioBob]

Sorry. Title says "FAR and Stock"

The moderator split this off from another thread because he believed we were getting off topic. He apparently thought we were starting a FAR vs. Stock debate, though that wasn't the case. I agree we may have wandered a bit OT, but the discussion has always been about stock aero.

[arkie87]

Incorrect. Drag force is proportional to mass x drag coefficient. If mass goes up while the drag coefficient goes down, then both quantities go up but not by the same proportion. In stock the difference is very small but it is there.

I think you misunderstood what i meant by "mass in not a factor". See below.

That is the misconception that I've been arguing against. It is not the magnitude of the drag force that determines how fast the vehicle slows down - it is the acceleration that the drag force produces, i.e. a = F/m. While adding parts increases the drag, it also increases the mass. Both together must be taken into consideration. It is not valid to make the blanket statement that increasing drag force increases drag losses. Drag force and drag loss are not the same thing.

I agree, but i was talking about the mass-averaged drag coefficient (which, for the reasons you explained above, is all that matters). So all that matters is whether drag coefficient of the added part are higher or lower than mass-averaged. If added part has drag coefficient above average, then part goes less distance; if not, it goes farther. If you think about it in terms of mass average drag coefficient, then mass is not a factor...

[Claw]

The moderator split this off from another thread because he believed we were getting off topic. He apparently thought we were starting a FAR vs. Stock debate, though that wasn't the case. I agree we may have wandered a bit OT, but the discussion has always been about stock aero.

Feel free to tell me what you'd like the thread to be titled. Or have Starman4308 change it.

[Starman4308]

Feel free to tell me what you'd like the thread to be titled. Or have Starman4308 change it.

My serious suggestion is "Effects of nosecones in stock aerodynamics". I'm in no rush to re-title it though.

The less-serious one is "Particularly minute minutiae of nosecones in stock aerodynamics".

[Claw]

The less-serious one is "Particularly minute minutiae of nosecones in stock aerodynamics".

Let it be so! No reason to be overly serious unless you want to. Feel free to change the title if you guys come up with something different.

My apologies if I so misunderstood the intended direction. Although I think everyone now has more breathing room in a separate thread.

Cheers,

~Claw

[OhioBob]

The less-serious one is "Particularly minute minutiae of nosecones in stock aerodynamics".

Sounds good to me.

[panzer1b]

Ive come to the conclusion that until aerodynamics changes (not sure how they work with FAR/NEAR), there is no point to nosecones outside of appearance. They are extra dead weight, the affect they have on total drag is more or less meaningless unles half your mass is the nosecone (in which case you are far better off swapping that extra mass for fuel), and ontop of that it adds to part count (its not like KSP isnt super optimized, it can so handle 1000 parts with 0 lag!).

I use them for looks, theyre good for that, otherwise, they stay off my designs (+ i dont make that many conventional rockets, and nosecones dont really do jack on a SSTO/plane)

[The_Rocketeer]

I took an OKTO2, and added either a 0.1t nosecone, or two 0.05t batteries. The one with the nosecone reached about 20 m/s faster peak velocity when dropped from 5 km (using Hyperedit).

There are no stock batteries that weigh 0.05t. Also, radial batteries are massless and consequently wouldn't have any effect in the experiment.

I think I can break this debate down into a really simple and understandable question, which will have a factual answer in the formula (for a mathematician to find):

Consider two objects, Object A with mass 1.0 and drag 0.1 and Object B with mass 1.0 and drag 0.2. If you drop them in an atmosphere, then even though the force of gravity on them is equal Object A will fall faster than Object B because it has less drag.

Now stick Object A to Object B to create object C. Here's the nub:

Does Object C have 2.0 mass and 0.3 drag (Slashy's argument: 0.1 + 0.2), or does Object C have 2.0 mass and 0.15 drag (OhioBob's argument: [0.1 + 0.2] / 2).

[Starman4308]

There are no stock batteries that weigh 0.05t. Also, radial batteries are massless and consequently wouldn't have any effect in the experiment.

Le Z-1k battery.

I think I can break this debate down into a really simple and understandable question, which will have a factual answer in the formula (for a mathematician to find):

Consider two objects, Object A with mass 1.0 and drag 0.1 and Object B with mass 1.0 and drag 0.2. If you drop them in an atmosphere, then even though the force of gravity on them is equal Object A will fall faster than Object B because it has less drag.

Now stick Object A to Object B to create object C. Here's the nub:

Does Object C have 2.0 mass and 0.3 drag (Slashy's argument: 0.1 + 0.2), or does Object C have 2.0 mass and 0.15 drag (OhioBob's argument: [0.1 + 0.2] / 2).

Depends on how you define drag. Is it the sum of (part mass * Cd), or is it the weighted-average Cd? For purposes of launch, the first definition (an absolute value) is more useful, while for purposes like terminal velocity, the second definition (effectively mass-normalized) is more useful.

[OhioBob]

The object without the nose cone will actually have a higher terminal velocity.

Incorrect. Adding a part with a lower Cd than the average will reduce the average Cd, which, in stock, means a higher terminal velocity.

I just performed an experiment that settles this. I launched a vehicle with two probes that I could detach and allow to free fall. Both probes included a remote control unit and a battery bank. The only difference was that one probe had an aerodynamic nose cone and the other didn't. I think the following images speak for themselves.

The probe without the nose cone actually started out with a very small lead, likely due to the ejection force of the decoupler, however the probe with the nose cone quickly overtook it and pulled away. Clearly the probe with the nose cone has the higher terminal velocity. This is because of that probe's higher ballistic coefficient, despite the fact that the drag force acting on it is greater.

Edited December 14, 2014 by OhioBob
spelling

[Norpo]

-snip-

Just did an experiment that mimics this; it's true.

(also, it'll go EVEN faster if you don't have a probe core at all, just a nosecone)

[OhioBob]

Does Object C have 2.0 mass and 0.3 drag (Slashy's argument: 0.1 + 0.2), or does Object C have 2.0 mass and 0.15 drag (OhioBob's argument: [0.1 + 0.2] / 2).

That's an incorrect restatement of my argument. I agree that if you attach Objects A and B the resulting Object C will have 2.0 mass and 0.3 drag. My argument is that Object B has 0.2 drag per unit mass, while Object C has 0.15 drag per unit mass. Since the drag per unit mass of Object C is lower than Object B, Object C will have a higher terminal velocity even though the drag force is higher.

[OhioBob]

I just performed a series of experimental launches to test the effect of launching with and without a nose cone. I used a rocket with a Mainsail first stage, a Skipper second stage, and a 14 t dummy payload. Everything was identical except for the addition of a nose cone in the one case. The nose cone was jettisoned along with the first stage at an altitude of about 12 km. After a couple practice launches to optimize my turn, I performed three launches each with and without a nose cone. That's not a big enough sample size to cancel out all the variables, but is still gives us some data to work with. Here's what I got.

No Nose Come: Launch vehicle ÃŽâ€V = 4748 m/s, ÃŽâ€V remaining after orbit insertion = 238 m/s, ÃŽâ€V required to reach orbit = 4510 m/s.

With Nose Come: Launch vehicle ÃŽâ€V = 4734 m/s, ÃŽâ€V remaining after orbit insertion = 224 m/s, ÃŽâ€V required to reach orbit = 4510 m/s.

I think these results are consistent with what most of us expected. Adding a nose cone reduces the ÃŽâ€V of the launch vehicle and leaves us with less ÃŽâ€V remaining at orbit insertion. However, we can see that the ÃŽâ€V required to reach orbit is unchanged. In theory I would have expected the required ÃŽâ€V to be slightly less with the nose cone, however the mass of the nose cone is so small in proportion to the rest of the rocket that the decrease in drag coefficent it provides is almost negligible. Perhaps with a larger sample size we would start to see a small effect.

In conclusion: Nose cones provide negligible aerodynamic advantage and are just needless added mass that harm the overall efficiency of a launch vehicle. I don't think this comes as a big surprise to anyone.

[The_Rocketeer]

Le Z-1k battery.

D'oh!

Blame the wiki parts table, which lists it as being 0.1 mass.

That's an incorrect restatement of my argument.

Actually, it's completely correct. Max_drag values (those listed as 'drag' in the part tooltips) are actually coefficients of drag for that part. Therefore, what you call drag (the mass-weighted drag coefficient) and what Slashy calls drag (the sum of max_drag values) are not the same thing.

If this difference of meaning had been pointed out earlier, it might have saved a lot of pointless debate. This is the very heart of the entire disagreement.

Nonetheless, I congratulate you on your ability to make (and demonstrate) a point.

[OhioBob]

Therefore, what you call drag (the mass-weighted drag coefficient)

If at anytime I've referred to the mass-weighted drag coefficient as "drag" then I misspoke. I think I have been fairly consistent in referring to that as "drag coefficient", or at least that has been my intent. When I have used the term "drag", or more specifically "drag force", I have meant it to be the force calculated by the formula F_d = ÃÂv²C_dA/2.

[Kesa]

Nose cone are intended to be heat sinkers for your straped SRBs:cool:

[The_Rocketeer]

If at anytime I've referred to the mass-weighted drag coefficient as "drag" then I misspoke. I think I have been fairly consistent in referring to that as "drag coefficient", or at least that has been my intent. When I have used the term "drag", or more specifically "drag force", I have meant it to be the force calculated by the formula F_d = ÃÂv²C_dA/2.

The confusion stems from the game's use of the term 'drag', which is the same for each part whether it is the coefficient or 'max_drag'.

For a single part the stated drag rating, or max_drag value, is, de facto, a drag coefficient: in my example Object A's mass-weighted drag coefficient is 1.0 (mass) * 0.1 (drag) / 1.0 (mass) = 0.1 (mass weighted drag coefficient), which is the same as the initial 'drag' value. Since other stated values for parts are cumulative (mass, lift rating, thrust, etc), it's reasonable for players (such as Slashy and myself) to assume that max_drag values are also cumulative.

Turns out not to be so because mass modifies both sides of the overall drag * mass : mass ratio.

So, don't feel criticised for being unclear - as consistent as you might have been, the way this information is presented in the game is such that if you say 'drag coefficient' many will read 'drag rating', because, per part, this is a technically correct interpretation.

In my example I was trying to link back to the values presented in game, which are listed simply as 'drag'. When you read these numbers, you're tempted to believe you're reading an absolute value that aggregates with other values in a rocket for a total rocket value. The whole disagreement between you and Slashy is basically whether that's the case or not, and as you've ultimately shown, it's not.

Edited December 15, 2014 by The_Rocketeer

[OhioBob]

For a single part the stated drag rating, or max_drag value, is, de facto, a drag coefficient: in my example Object A's mass-weighted drag coefficient is 1.0 (mass) * 0.1 (drag) / 1.0 (mass) = 0.1 (mass weighted drag coefficient), which is the same as the initial 'drag' value. Since other stated values for parts are cumulative (mass, lift rating, thrust, etc), it's reasonable for players (such as Slashy and myself) to assume that max_drag values are also cumulative.

Your example confused me because your meaning of the term "drag" was not clear. In my way of thinking, max_drag = drag coefficient, while "drag" is proportional to Cd * mass. Since you used a mass of 1 for both objects, then the values of max_drag and Cd * mass were the same. Although the max_drag values are not cumulative, max_drag * mass is. You happened to use an example where it was impossible to discern your meaning.