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HARP fired projectiles from a gun into suborbital trajectories. This type of projectile carried a scientific payload, but did not have any reaction engines (although later proposals did). Their designs evolved over the years, but it seems like the general shape of the projectile was always in a genetic rocket shape, similar to this:

enter image description here

How does a rocket shape make any sense, considering that this didn't have engines? The drag coefficient of this shape looks to be about 0.75. On the other hand, alternative shapes have lower coefficients:

drag coefficients

If we were to superficially accept these numbers, HARP could have achieved a significant reduction in atmospheric losses by switching to a droplet shape, possibly by a full order of magnitude.

The fins obviously have some role, but I don't see how they impact this discussion. If you have a tapered end, that could still have fins. Stability of its orientation is obviously important - does that restrict the shape? Or, does the modeling of drag coefficient fundamentally change at several mach numbers, so that there would be no benefit to the tapered end? To my knowledge, all projectiles had a disposable portion that held it in place as it moved through the barrel, so it seems like that would make any shape practically workable.

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    $\begingroup$ Where do you get a drag coefficient of 0.75 from for what's essentially a dart-shaped ballistic missile with bottom stabilizing fins? It doesn't seem right, should be much closer to a streamlined body. $\endgroup$
    – TildalWave
    Feb 14, 2014 at 14:16
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    $\begingroup$ @TildalWave No it shouldn't, not unless you're using some weird definition of area. It's not the front that matters, it's the back. Given that, it's not that dissimilar to other shapes like a sphere, which is around 0.5. $\endgroup$
    – AlanSE
    Feb 14, 2014 at 14:38
  • $\begingroup$ OK, true, but HART missile has maximum Cd of about 0.5 at a bit over Mach 1. I can easily agree with your assessment later on, it's just that Cd of 0.75 seems really high for what should surely be below 0.5 for a highly elongated body. $\endgroup$
    – TildalWave
    Feb 14, 2014 at 14:49
  • $\begingroup$ @TildalWave Agreed, 0.5 seems much more reasonable than 0.75. The cone is the best analog in the image, and it's 0.5 too. I found the 0.75 from that Wikipedia link, which references this NASA page, which gives the number for a model rocket exploration.grc.nasa.gov/education/rocket/termvr.html But perhaps that includes skin friction due to the long barrel? $\endgroup$
    – AlanSE
    Feb 14, 2014 at 15:27
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    $\begingroup$ $C_D$ by itself is not the parameter of interest. It is the ballistic coefficient, $m\over C_D A$ that will determine how far, fast, high the thing goes. If we assume that we will compare shapes that are the same mass, then it is $C_D A$ that matters. A sphere of the same mass will have a much larger $A$, so you can't just compare $C_D$'s. $\endgroup$
    – Mark Adler
    Feb 14, 2014 at 19:25

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The "rocket shape" dart has a significantly lower drag coefficient than the cylinder or the shown 45° cone. It's still above the teardrop, but those drag coefficients are for subsonic regimes.

Once one gets into transonic and supersonic flight regimes, the major issue isn't atmospheric flow, but shockwave turbulence. HARP's projectiles were well into the supersonic.

As with all supersonic bodies, the shockwave has to remain clear of the body for minimum turbulence, and the longer and narrower shape does that. A gentle continuous curve also allows the maximum volume at designed optimal speed. As an unpowered projectile, the shockwave can be kept clear of the entire body.

There is a reason to have the very back less aerodynamic - stability. The area inside the shockwave isn't free of motion, but is much reduced airflow. So, a slightly higher drag at the aft keeps the nose pointed forward without spin stabilization. Further, it can allow for control surfaces, though that isn't always utilized in research projectiles.

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