⚡ electrical engineering

Aerodynamic and Ballistic Analysis of a 155 mm Rocket-Assisted Projectile

This study utilizes validated CFD simulations and ballistic modeling to demonstrate that the exhaust plume of a 155 mm Rocket-Assisted Projectile significantly alters base flow aerodynamics, increasing drag by up to 90% and reducing maximum range by approximately 720 meters, thereby providing a framework for optimizing propulsion systems to enhance artillery performance.

Original authors: Lucas Gomes do Amaral, Victor Santoro Santiago, André Luiz Tenório Rezende

Published 2026-08-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Lucas Gomes do Amaral, Victor Santoro Santiago, André Luiz Tenório Rezende

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to throw a heavy stone as far as possible. You know that if you throw it too hard, the air pushes back against it, slowing it down. This pushback is called "drag," and it's the invisible enemy of anything trying to fly fast. Now, imagine you could strap a tiny, powerful rocket to the back of that stone to give it a second wind mid-air. That's the idea behind a "Rocket-Assisted Projectile" (RAP). It's like giving a sprinter a jetpack for the middle of the race. But here's the tricky part: when that rocket fires, it shoots out a hot, messy cloud of gas called an "exhaust plume." This plume doesn't just push the rock forward; it also messes with the air swirling around the back of the rock. It's like trying to run through a crowd while someone is blowing a giant, chaotic fan right behind your head. The big question for scientists is: Does this messy air cloud help the rocket go farther, or does it actually make the air push back harder, slowing the whole thing down?

This paper dives into that exact mystery using a 155 mm artillery shell, a type of big cannonball used by armies. The researchers, working at the Military Institute of Engineering in Brazil, wanted to see what happens when you fire a rocket-assisted shell at supersonic speeds (faster than the speed of sound). They didn't just shoot real shells; instead, they built a super-detailed virtual world inside a computer. They used a method called Computational Fluid Dynamics (CFD), which is basically a high-tech way of simulating how air flows around objects, to watch how the rocket's exhaust cloud interacts with the fast-moving air. They compared a shell with a rocket firing to one without, checking how the air pressure changed at the back of the shell and how much "drag" (air resistance) was created. They then fed these numbers into a ballistic calculator to see how far the shell would actually fly in real life.

Here is the surprising twist the paper found: the rocket exhaust, which is supposed to be the hero that pushes the shell farther, actually creates a bit of a villainous side effect. When the rocket fires, the hot exhaust cloud changes the way the air swirls behind the shell. Instead of a smooth, quiet wake, the exhaust creates a more compact, turbulent mess that actually increases the air resistance significantly. In the simulations, the researchers found that when the rocket was firing, the aerodynamic drag increased by about 70% to 90% compared to when the rocket wasn't firing, especially at lower speeds (between Mach 0.7 and 1.0). As the shell got faster (up to Mach 2.5), this extra drag became less of a problem, but it was still there.

Think of it like this: The rocket engine is like a strong friend pushing you from behind, but the exhaust cloud is like that friend accidentally tripping over your shoelaces, creating a huge drag on your feet. The push is good, but the trip is bad. The paper shows that this "trip" is real and measurable. When the researchers ran 3,300 different flight simulations to see how far the shell would go, they found that this extra drag caused by the exhaust cloud actually shortened the maximum distance the shell could travel. For the best firing angles, the shell flew up to 720 meters shorter than it would have if the exhaust cloud didn't mess with the air so much.

The study also looked at when this happens. The extra drag only matters while the rocket is burning, which is a short burst of time (about 3 seconds) early in the flight. If you fire the shell at a low angle, it hits the ground before the rocket even turns on, so the exhaust doesn't matter. But if you fire it high into the air, the rocket burns while the shell is still climbing, and that extra drag adds up, stealing distance from the final landing spot. The researchers were very careful with their math, checking their computer models against known data to make sure their simulations were accurate. They found that their computer models were reliable, with very small errors, so they are confident that this "exhaust penalty" is a real physical phenomenon, not just a glitch in the code.

So, what's the takeaway? If you are designing a rocket-assisted shell, you can't just look at how much thrust the rocket makes. You have to look at the messy, hot cloud it leaves behind. That cloud changes the air pressure at the back of the shell, making it harder to push through the sky. The paper suggests that ignoring this effect would make you think your shell will fly farther than it actually will. By understanding this interaction, engineers can tweak the rocket nozzle or the timing of the ignition to try and minimize this drag penalty, helping these high-tech shells reach their true potential. It's a reminder that in the world of high-speed flight, even the things pushing you forward can sometimes create a little bit of trouble for you along the way.

Technical Summary: Aerodynamic and Ballistic Analysis of a 155 mm Rocket-Assisted Projectile

Problem Statement
Rocket-Assisted Projectiles (RAPs) are critical for extending the range of field artillery without requiring barrel modifications. However, the interaction between the rocket exhaust plume and the external supersonic flow generates complex aerodynamic phenomena that are not fully understood. While the propulsion system provides thrust, the exhaust gases alter the base pressure, wake structure, and recirculation regions, potentially increasing aerodynamic drag. Despite the strategic importance of RAPs, open literature contains limited experimental and numerical data quantifying these plume-flow interactions and their specific impact on projectile range and trajectory. This study addresses the gap in understanding how propulsion-induced modifications to the base flow affect the overall ballistic performance of a 155 mm RAP.

Methodology
The authors employed an integrated approach combining Computational Fluid Dynamics (CFD) with a Modified Point-Mass ballistic solver.

CFD Simulation: Reynolds-Averaged Navier-Stokes (RANS) equations were solved using the SST $k-\omega$ turbulence model for a 155 mm projectile geometry. Simulations covered a Mach number range of 0.7 to 2.5 for both propelled (with exhaust) and non-propelled configurations. The projectile geometry was reconstructed based on dimensions reported by Ferfouri et al., with a convergent-divergent nozzle added to the base for the propelled cases. The rocket motor utilized a "Neutral" thrust profile with a total pressure of 20 MPa and temperature of 2900 K.
Numerical Verification: To ensure reliability, a mesh independence study was conducted using three resolution levels (coarse, medium, fine). Numerical uncertainty was quantified using the Grid Convergence Index (GCI) methodology. The unpropelled CFD results were validated against reference data from the PRODAS industrial software.
Ballistic Simulation: A Modified Point-Mass model based on STANAG 4355 was used to simulate 3,300 trajectories. Three aerodynamic databases were compared:
1. PRODAS baseline coefficients.
2. CFD coefficients for the unpropelled configuration.
3. CFD coefficients for the propelled configuration (where drag coefficients were updated to reflect plume effects only during the motor burn period).
  The simulations varied launch elevations from 1 to 1100 mils to assess performance across the operational envelope.

Key Results

Aerodynamic Impact: The presence of the exhaust plume significantly altered the wake topology, creating a more compact recirculation region and reducing base pressure. This resulted in a substantial increase in aerodynamic drag compared to the non-propelled configuration.
- In subsonic and transonic regimes (Mach 0.7–1.0), the drag coefficient for the propelled configuration was approximately 70% to 90% higher than the baseline.
- As the Mach number increased, the relative difference in drag decreased. This is attributed to the fact that base pressure in the unpropelled configuration naturally decreases at higher speeds; thus, the additional pressure reduction caused by the plume represents a smaller relative change.
- Thrust predictions showed excellent convergence with GCI values near 0.1%, indicating that the drag increase was the dominant uncertainty factor rather than propulsion modeling.
Ballistic Consequences: The inclusion of plume-induced drag in the trajectory solver revealed a measurable reduction in maximum range.
- For low-elevation trajectories, the plume had negligible effect because the projectile impacted the ground before motor ignition.
- For higher firing angles (where the motor burns during flight), the range reduction increased with elevation, reaching a maximum loss of approximately 720 meters near optimal firing angles.
- The divergence in trajectories and velocity loss occurred primarily during the first 50 seconds of flight (the powered phase). After motor burnout, the trajectories converged as the aerodynamic conditions returned to the unpropelled state.

Significance and Claims
The paper claims that neglecting the aerodynamic penalty of the exhaust plume leads to an overestimation of the ballistic performance of rocket-assisted projectiles. The study demonstrates that while the propulsion system adds energy, the associated modification of the base flow introduces a significant drag penalty that partially offsets these gains.

The authors assert that accurate prediction of plume-induced aerodynamic effects is essential for realistic trajectory prediction and performance assessment. The proposed CFD-ballistic framework serves as a practical tool for future optimization studies, specifically regarding nozzle geometry, ignition timing, and motor operating conditions, to enhance the performance of extended-range artillery systems. The work emphasizes that the interaction between the exhaust plume and external flow must be considered during the aerodynamic characterization and design phases of RAPs.

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