---
title: "Ballistic limit"
chunk: 1/1
source: "https://en.wikipedia.org/wiki/Ballistic_limit"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T11:45:41.342801+00:00"
instance: "kb-cron"
---

The ballistic limit or limit velocity is the velocity required for a particular projectile to reliably (at least 50% of the time) penetrate a particular piece of material.  In other words, a given projectile will generally not pierce a given target when the projectile velocity is lower than the ballistic limit.  The term ballistic limit is used specifically in the context of armor; limit velocity is used in other contexts.
The ballistic limit equation for laminates, as derived by Reid and Wen is as follows:

  
    
      
        
          V
          
            b
          
        
        =
        
          
            
              π
              
              Γ
              
              
                
                  
                    ρ
                    
                      t
                    
                  
                  
                  
                    σ
                    
                      e
                    
                  
                
              
              
              
                D
                
                  2
                
              
              
              T
            
            
              4
              
              m
            
          
        
        
          [
          
            1
            +
            
              
                1
                +
                
                  
                    
                      8
                      
                      m
                    
                    
                      π
                      
                      
                        Γ
                        
                          2
                        
                      
                      
                      
                        ρ
                        
                          t
                        
                      
                      
                      
                        D
                        
                          2
                        
                      
                      
                      T
                    
                  
                
              
            
            
          
          ]
        
      
    
    {\displaystyle V_{b}={\frac {\pi \,\Gamma \,{\sqrt {\rho _{t}\,\sigma _{e}}}\,D^{2}\,T}{4\,m}}\left[1+{\sqrt {1+{\frac {8\,m}{\pi \,\Gamma ^{2}\,\rho _{t}\,D^{2}\,T}}}}\,\right]}
  

where

  
    
      
        
          V
          
            b
          
        
        
      
    
    {\displaystyle V_{b}\,}
  
 is the ballistic limit

  
    
      
        Γ
        
      
    
    {\displaystyle \Gamma \,}
  
 is a projectile constant determined experimentally

  
    
      
        
          ρ
          
            t
          
        
        
      
    
    {\displaystyle \rho _{t}\,}
  
 is the density of the laminate

  
    
      
        
          σ
          
            e
          
        
        
      
    
    {\displaystyle \sigma _{e}\,}
  
 is the static linear elastic compression limit

  
    
      
        D
        
      
    
    {\displaystyle D\,}
  
 is the diameter of the projectile

  
    
      
        T
        
      
    
    {\displaystyle T\,}
  
 is the thickness of the laminate

  
    
      
        m
        
      
    
    {\displaystyle m\,}
  
 is the mass of the projectile
Additionally, the ballistic limit for small-caliber into homogeneous armor by TM5-855-1 is:

  
    
      
        
          V
          
            1
          
        
        =
        19.72
        
          
            [
            
              
                
                  7800
                  
                    d
                    
                      3
                    
                  
                  
                    
                      [
                      
                        
                          (
                          
                            
                              
                                e
                                
                                  h
                                
                              
                              d
                            
                          
                          )
                        
                        sec
                        ⁡
                        θ
                      
                      ]
                    
                    
                      1.6
                    
                  
                
                
                  W
                  
                    T
                  
                
              
            
            ]
          
          
            0.5
          
        
      
    
    {\displaystyle V_{1}=19.72\left[{\frac {7800d^{3}\left[\left({\frac {e_{h}}{d}}\right)\sec \theta \right]^{1.6}}{W_{T}}}\right]^{0.5}}
  

where

  
    
      
        
          V
          
            1
          
        
      
    
    {\displaystyle V_{1}}
  
 is the ballistic limit velocity in fps

  
    
      
        d
      
    
    {\displaystyle d}
  
 is the caliber of the projectile, in inches

  
    
      
        
          e
          
            h
          
        
      
    
    {\displaystyle e_{h}}
  
 is the thickness of the homogeneous armor (valid from BHN 360 - 440) in inches

  
    
      
        θ
      
    
    {\displaystyle \theta }
  
 is the angle of obliquity

  
    
      
        
          W
          
            T
          
        
      
    
    {\displaystyle W_{T}}
  
 is the weight of the projectile, in lbs


== References ==