# Understanding Transonic Flight

The flight of a rifle bullet may seem to be a simple thing – it flies through the air at high speeds, steadily losing velocity and energy until it either impacts the dirt or simply falls out of the sky. In fact, though, there is a lot of complex fluid dynamics to absorb to fully understand the flight of a bullet through the air, especially as that bullet drops below Mach 1.3 (about 1,450 ft/s) and encounters the transonic flight regime. To help us understand what happens better, we’ll turn to an instructional video from the 1950s from Shell Oil; while it covers the flight of then-high-performance aircraft, not bullets, the basic principles still remain the same. I highly recommend my readers watch the video first, before reading my discussion of it:

The flow animations shown in the video illustrate perfectly the fluid dynamics of transonic airflow over wings. These animations apply to bullets, as well, however the flow is radial, around the bullet, instead of linear as along a wing. One of the effects noted in the video – flow separation – will affect bullets in a similar way as wings; bullets as they travel beyond the high point in their trajectory fly through the air with a positive angle of attack – they are canted upwards – as they are stabilized by the rifling. Therefore, they are generating some lift, just like a wing (though much, much less). When they enter the transonic flight regime, they will experience flow separation, which can seriously affect their accuracy during that part of flight.

A bullet’s shape can be improved for supersonic flight, just like an airplane’s can. Unlike an airplane, a bullet does not have wings or other significant protrusions, and therefore area ruling is expressed more subtly. We can see how area ruling might work on a bullet, shown below:

This is a radial section of a flat-based, tangent ogive conventional bullet. We can see that the bullet’s shape does not conform well to the curve inscribed on it on the right. Area ruling is needed to bring the bullet’s shape closer to that of the curve, reducing drag and improving the bullet’s transonic characteristics.

The same bullet, area-ruled to the curve. A boattail has been added in the correct location to conform closely to the shape of the curve, and the ogive has been changed to a secant-type matching a section of the curve. This bullet will have a much higher ballistic coefficient, and be more resistant to transonic buffeting – thanks to it having a higher critical Mach number, improving its long-range accuracy and hitting power.

We can see a similar shape expressed in this Luftwaffe F-104G Starfighter. The F-104 was one of the earliest fighters designed through a good understanding of supersonic airflow; in dramatic contrast to earlier high-speed aircraft, it possesses an area-ruled fuselage, sharp angles, thin wings, and an all-moving tailplane set high on the vertical stabilizer. Image source: wingsovereurope.com.

With careful bullet design, transonic buffeting can be reduced or nearly eliminated, dramatically improving long-range accuracy. Further, in doing so drag can be dramatically reduced, leading to greatly improved long-range velocity and striking power.

Unlike a plane, a bullet does not fly at low speeds, then accelerate to high speeds, then decelerate to low speeds again; throughout its flight, the projectile of a rifle decelerates. What this means is that the description of a rifle crack as “the noise a bullet makes when it breaks the sound barrier” is not quite correct; a bullet actually crosses the sound barrier from supersonic flight to transonic flight. In fact, the crack of a rifle is a sonic boom, just like that produced by an airplane, and is generated throughout the bullet’s supersonic flight path.

Certainly, a someone trying to create refined understanding of small arms should not restrict themselves only to material pertaining directly to it; physics applies everywhere, and older learning aids like this one can be a big help improving your understanding of a topic.

#### Nathaniel F

Nathaniel is a history enthusiast and firearms hobbyist whose primary interest lies in military small arms technological developments beginning with the smokeless powder era. In addition to contributing to The Firearm Blog, he runs 196,800 Revolutions Per Minute, a blog devoted to modern small arms design and theory. He is also the author of the original web serial Heartblood, which is being updated and edited regularly. He can be reached via email at nathaniel.f@staff.thefirearmblog.com.

• Blake

awesome article, thanks

• Zugunder

All I need to know about bullets is that I don’t want to block their path. Seriously tho, great article, thanks!

• MPWS

One item though is HOW larger caliber pistol bullets with their stubby nose and poor length to diameter ratio fall into this theory. And they are often supersonic too.
The other thing to consider is the fact, that bullets are supersonic (several times actually) and became such, while in protected environment of barrel. All they have to do is to punch thru stale air wall at the exit which is much simpler task then what Aircraft goes thru; so the comparison is not really pertinent. This applies for any type and shape by the way – and they fly.

Do I make it too complex, or too simple? :-)))

• Ethan

Anything can be supersonic – even a brick. But not many un-engineered things can be have a high Ballistic Coefficient. Fitting the shape of the projectile to the fluid “curve” as shown in the picture above is the job of ballistics engineers – and it takes advanced modelling software like ANSYS.

Even the very best software on the market today is still only a good guess of what happens in the transition between supersonic and subsonic flight. Kind of like Turbulent flow modeling – there’s still a lot of the WHY we don’t understand about it, but on the whole they have learned to predict it with reasonable accuracy.

• MPWS

I supplied following contribution on subject of transition from supersonic to subsonic (concerning laminar and turbulent flow) and on fluid mechanics in general. Yet, editor is holding back on it. there was nothing personal in it nor political. But I am not registered, true.

• MPWS

BTW, thanks for fair response.

• -V-

I think the simple answer is that pistol bullets are inherently inaccurate because they have poor aerodynamics. While its not a big deal at normal handgun distances, over rifle-type distances you would begin to appreciate their significantly worse flight characteristics. Otherwise, they fall exactly the same into this framework as optimized rifle bullets, jet fighters, and bricks hurled at supersonic speeds.

• MPWS

When you say “inaccurate” what do you mean by that? Should I interpret it that stubbier shorter projectile will have more tendency to deviate from intended path because it has worse form factor? (form factor being combination of B.C. and section density)
All I know is that it will exhibit tendency to loose speed more quickly.

• -V-

That’s my understanding as well. Pistol bullets have two things working against them: They start in trans-sonic flight, and they have fairly poor form factor. This means they start in a speed zone where you get a lot of the trans sonic shock wave issues described in the video (disclaimer: i’m not an aeronautical engineer so a lot of the nuance is lost on me) and they have a fairly poor form factor which means they get affected more by trans-sonic shock waves that will cause them to have a more erratic flight path. Not a big deal at 25 yards but at say 250 yards they would be expected to be performing noticeably worse then more streamlined and fast moving rifle bullets.

Also, the poor form factor greatly increases drag on the projectile and causes it to loose speed more quickly. So a bit of a “double-whammy”.

I think it was more as it pertains to long range shooting and how it can affect accuracy if you shoot at a distance where your particular caliber and loading slows down into that trans sonic range.

So, on 5.56 for instance, if you wanted to shoot for accuracy (obviously lethality drops off with loss of speed), past six or seven hundred yards, that trans sonic instability is going to affect performance.

• MPWS

I think so too. It seem to come to together.
As you say it is behaviour during transition period (if it happens) which may make the difference.

• HMSLion

Few pistol rounds operate in the true supersonic regime. Most are transonic, and all bleed velocity like a stuck pig. Between base drag (the partial vacuum at the aft end of the bullet), and a front end design optimized for terminal ballistics, aerodynamics gets very low priority.

• MPWS

True. Yet as you can see, when used in carbines, they perform satisfactorily at 200yrds, mostly noted as practical “slug-fest” range.

• Micki

I noticed that when Jerry Miculek performed his 1000-yard 9mm revolver shot, he used 147gr Hornady XTP subsonics.

• Ye Ole CRAB

Interestingly enough, WW II studies of the 45 ACP tracer, found the
benefits of “BASE BLEEDERS” to fill this vacuum. Many large caliber
artillery projectiles have a chemical fire compound to produce gasses
and help with the drag factor. HMS Lion is correct in mentioning the
effect. More study should be done on small caliber long range bullets

• Andrew

• d_grey

A good read, gave a good understanding of projectile physics.

Good stuff. For us older critters, it was also nice to see all of those airplane models again.

• uisconfruzed

Great article, thanks

• nova3930

Gah I’m having flash backs to Jr year compressible aerodynamics. When density becomes variable gases do some crazy things especially in nozzles and pipe flow.

• The F -104 didn’t use area rule in it’s design.

• Just consulted with my aero/astro buddies, Phil; the F-104 was area-ruled.

• I believe the F-104 was area ruled, but it didn’t require a dramatic Coke bottle shape because the wings were very thin. I will check with my aero/astro buddies, though.

• Martin Grønsdal

could the bullet have a shape where the rear mimics the front?

would that be better for supersonic flight?

or, would the exploding gunpowder affect that shape?

• gunsandrockets

I often wondered how a boat tailed bullet could aid the performance of a supersonic rifle bullet. Area ruling and transonic drag! Very enlightening.

Funny how those pre-WWI innovators stumbled upon such an important improvement of rifle bullets.

• gunsandrockets

“Some critics say the F-104 doesn’t have enough range. … With the same 4 tanks, climbing to 21 km and accelerating to Mach 2, the plane can cover nearly 2300 km. With 1300 of that at Mach 2.”

Perhaps I am off base, but that sounds very exaggerated.

Based upon the flight data I found at the other link, an F-104 with tip tanks consumes 250 pounds of fuel per minute at Mach 2 at 50,000 feet. So over a 1300 km distance at Mach 2 equals over 10,000 pounds of fuel consumed!

Since that same link says the Starfighter has a maximum fuel load of 10,000 pounds, and says 4,000 pounds is consumed from take-off to Mach 2 at 50,000 feet, the total range range at 15 km altitude is more like 1,100 km and only 750 km of that at Mach 2.

• Rodford Smith

The data came from a fellow who flew the plane and kindly got out his old manuals and looked up the ferry data for me. I don’t recall offhand if he included the ferry kit’s additional internal tanks in his calculations, but he did definitely include both wingtip and pylon tanks.

• Guest