**34. Scenario 3—frontal
hit immediately after rear hit**

This third scenario is the overt combination of a rear hit
that does everything followed immediately by a frontal hit that adds only
momentum (frontal scenario 1).
This is the version proposed by Josiah Thompson in *Six Seconds in Dallas*.
The rear hit snaps the head forward, then explodes the head and creates the
cloud and the two large fragments. Its proponents do not claim that it also
creates the lurch, but this monograph shows that it must create a sizeable
lurch. The frontal hit then simply adds momentum to the lurch. The question
considered here
is what happens when these two scenarios are combined into a single set of
equations, not just considered separately. The answer is that the two effects
combine linearly, and so can continue to be considered separately for
simplicity.

**The procedure for calculating**

Scenario SL6L was chosen for simplicity, so as to avoid having
to deal with the tricky *R _{head}* and

The modified conservation equations are shown below. Since the second bullet was not part of the explosion caused by the first bullet, it did not participate in it directly. That means that it only had to added to the equation for conservation of momentum.

**The results**

The results of using these new equations can be expressed very
simply, for the equations represent the combination of scenario SL6L with new
scenario 1 for the frontal hit. We test whether the joint equations give the
same answers as the equations used separately. If they do, the extra lurch from
the frontal shot can just be added to the lurch from the rear shot, and there is
no more need to use these combined equations.

The table below shows the results. The lurches are strictly
additive, and the velocities of the cloud are additive by default, since the
frontal hit does not contribute to the lurch from the rear hit. These results
mean that these two scenarios add to one another, and can be considered
separately. The rear hit creates a rearward lurch of 1.05 ft s^{-1}. The
frontal hit creates a rearward lurch of 0.17 ft s^{-1} by itself. The
two bullets combined create a lurch of 1.22 ft s^{-1}, which is just the
sum of 1.05 and 0.17.

Scenario |
v, ft s_{lurch}^{-1} |
v, ft s_{cloud}^{-1} |

Rear hit from MC |
-1.05 | 406 |

Frontal hit from XP-100 |
-0.17 | — |

Rear and frontal hits together |
-1.22 | 406 |

Ahead to Scenario 4

Back to Scenario 2

Back to Physics of the Head Shot