**SECONDARY SLAP
- TWO COLLISIONS OR ONE?**

** **

Copyright Ó George
M. Bonnett, JD 1998 All Rights Reserved

One of the nightmares of anyone investigating
vehicular collisions is the case in which one of the vehicles rotates after the
collision and there is secondary contact between the two vehicles. The term generally applied to this contact
is "secondary slap."

This secondary slap is generally relatively close to
the separation of the two vehicles after their initial contact in both distance
and time. It usually involves much less
force than the initial collision, but creates a much greater problem for the
investigator than the initial collision.
The problem is that, in the past, we have always had to treat them as
separate collisions. After all, we have
four different departure angles from two different collisions, and that creates
havoc in the linear momentum computations.

In dealing with the four different departure angles,
we must also deal with the fact that we have four different departure
speeds. For this reason, the safest way
to handle the problem was to make two separate problems out of this type of
collision.

At this point, it is necessary to say a word about ** vectors**
and

In a linear momentum computation, we use the Law of
Conservation of Linear Momentum. This
law states that the total momentum into collision must be equal to the total
momentum out of the collision (**P _{R }**

First, we must handle the secondary slap as a linear
momentum problem in order to obtain the necessary information to deal with the
primary collision. This involves a
determination of the departure angles out of the secondary slap and a
determination of the separation speeds from the secondary slap. We can use this information along with the
approach angles of the centers of mass of the vehicles into the secondary slap
in order to determine the speeds of the two vehicles at the impact of the
secondary slap.

The impact speeds of the centers of mass at the
secondary slap should be very close to the post impact speeds of the centers of
mass out of the primary collision, certainly within the margins of error
mandated by the uncertainty of the measurements. Due to the close proximity in both distance and time of the primary
collision to the secondary slap, the effects of the coefficient of friction
between the vehicles and the surface should be minimal.

Now we are able to tackle the linear momentum
problem involved in the primary collision.
The post impact speeds are known, as they are the pre-impact speeds
determined in the problem involving the secondary slap. The departure angles of the centers of mass
of the two vehicles out of the primary collision will usually be very close to
the approach angles of the two vehicles into the secondary slap.

This leads to an apparent contradiction. How can the departure angles out of the
primary collision and the approach angles into a secondary slap be the
same? This is possible because of the
same attribute that causes the secondary slap.
It is the shape of each of the two vehicles and the changing orientation
of these individual shapes about the center of mass of each vehicle that makes
this apparent contradiction possible.
The centers of mass are departing a collision based on the orientations
of the shapes of the vehicles and at the same time approaching a second
collision based on the orientation of the vehicles for the secondary collision.

With known departure angles and speeds for the
primary collision, the only unknowns are the approach angles for the primary
collision. Once these have been
measured, the impact speeds for the primary collision can be computed.

The method described above will certainly give us
impact speeds, and if all of our measurements have been accurate, should give
us accurate speeds, at least within the margin of error resulting from the
uncertainty of our measurements.
However, is all of this necessary?

Let us examine the above collision using a slightly
different approach. The law of
Conservation of Linear Momentum will still be our primary tool in this
re-examination of the collision, and in fact, it is this very law that must be
invoked in order to re-examine the collision.

In the secondary slap, which is truly a separate collision,
what really happened was an exchange of momentum between the two vehicles. In fact, this is what happens in all
collisions. The force that results in
the transfer of momentum from one vehicle to the other is called ** impulse**. This impulse is equal in magnitude and
opposite in direction for each vehicle.
It is an equal exchange between the two vehicles and results in their
individual momentum vectors being altered.
Because the impulse is equal, the change in the momentum vectors must
also be equal. Consequently, there is
no change in the resultant vector.
This, remember, is the Law of Conservation of Linear Momentum - the
momentum before impact and the momentum after impact must be the same

What effect does this have on our approach to
solving the problem? It has the effect
of allowing us to use the post impact information, the angles and speeds, from
the secondary slap as the post impact information for the primary collision. If the post impact resultant vector of the
secondary slap is identical to the pre-impact resultant vector for the
secondary slap, and the post impact resultant vector from the primary collision
is the pre-impact resultant vector for the secondary slap, then the post impact
resultant vector from the primary collision must be identical to the post
impact resultant vector for the secondary slap, and therefore, interchangeable.

Law of Conservation of Momentum:

** **

**P1 + P2 = P1' + P2'**

** **

**P11 + P22 = P11' + P22'**

** **

*If *

**P1' = P11**

*and *

**P2' = P22**

*then*

**P1' + P2' = P11' + P22'**

*THEREFORE:*

**P1 + P2 = P11' + P22'**

** **

What does not follow is that the post-impact
momentum vector for vehicle 1 out of the primary collision (**P1'**) is the same as the post-impact
momentum vector of vehicle 1 out of the secondary slap (**P11'**). Nor would it be
correct to say that the post-impact momentum vector for vehicle 2 out of the
primary collision (**P2'**) is the same
as the post-impact momentum vector of vehicle 2 out of the secondary slap (**P22'**).
Indeed, because the departure angles of the vehicles out of the primary
collision will probably be different from the departure angles of the vehicles
out of the secondary slap, the departure speeds of the vehicles out of the
collisions should likewise be different.

It would be correct therefore to say that in most
circumstances:

**P1' <>
P11'**

*and*

**P2' <>
P22'**

where **<>**
indicates **INEQUALITY**.

Therefore, it would be improper as well as
inaccurate to use the departure angle of one of the vehicles out of the primary
collision in combination with the speed of this vehicle out of the secondary
slap.

In other words, we may correctly use the post impact
data out of the primary collision or the post impact data out of the secondary
slap in order to determine the impact speeds of the vehicles at impact in the
primary collision. We cannot interchange the individual components of the post
impact data between the primary and secondary collisions.

This is a case of being able to act as if we are
ordering from a menu. We are allowed
take two vectors from either column A (**P1'**
and **P2'**) or column B (**P11'** and **P22'**), but we do not have the option of taking any two of the four
vectors to inject into the equation in order to reach a solution. We are limited to picking two vectors from the
same collision, but it may be from either the primary collision or the
secondary collision.

By studying the underlying fundamental principles
involved, we can see that the solution is not necessarily as complicated as it
first appears. While the rules
involving the application of the Law of Conservation of Momentum must be
strictly adhered to, they may also be used to eliminate computations that
merely become redundant.

Copyright Ó
George M. Bonnett, JD 1998 All Rights Reserved