Method for predicting ball launch conditions
The present invention relates to a method and a numerical analysis for predicting golf ball launch conditions, e.g., velocity, launch angle and spin rate. By acquiring pre-impact swing conditions, e.g., club speed, rotational rate and ball hit location, along with pertinent club features, e.g., moment of inertia, and ball impact features, e.g., normal and transverse forces as well as time of contact, the method can predict the resulting trajectory and launch conditions of the golf ball. The predicted ball launch conditions and trajectories can also be used to modify one or more properties of the golf ball or golf club. The time of contact measurements can be corrected to account for drag force.
1. A method for predicting velocity, launch angle and/or spin rate of a golf ball following an impact with a golf club or a slug comprising the steps of
a. determining at least one pre-impact swing conditions;
b. determining at least one property of the golf club;
c. calculating a normal force of the impact in a normal direction;
d. calculating a transverse force of the impact in a transverse direction; and
e. predicting the velocity, launch angle and/or spin rate from steps a-d;
wherein the force deformation equation based on Hertzian force deformation equations for step (c) is
F
=
K
(
ξ
a
)
β
(
1
+
A
(
ξ
a
)
2
)
(
1
+
α
ξ
.
a
)
wherein ξ=ball deformation,
a=ball radius and
β ranges from about 1.2 to about 1.5.
wherein, the ratio of (ξ) to a is greater than ⅓ and the dampening constant, α, is calculated using the following equation:
α
=
α
1
+
α
2
V
normal
wherein V normal is the initial velocity of relative impact.
2. The method of claim 1 , wherein the force deformation equation for step (d) is
F
T
=
K
T
(
ξ
N
a
)
1
/
2
(
ξ
T
a
)
(
1
+
A
T
(
ξ
T
a
)
2
)
(
1
+
α
T
ξ
.
T
a
)
wherein ξ=ball deformation, and
a=ball radius.
3. The method of claim 2 , wherein F T can be determined by measuring the spin rates of a plurality of golf balls striking the golf club or slug at different loft angle and velocity.
4. The method of claim 2 , wherein a ratio of F T /F N is directly related to the coefficient of friction of the impact.
5. The method of claim 1 , wherein a coefficient of restitution of the impact is measured and the α 1 and α 2 factors are derived from the measured coefficient of restitution.
6. The method of claim 1 , wherein a time of contact of the impact is measured and the K and A factors are derived from the measured time of contact and the time of contact is corrected for drag force.
7. The method of claim 1 , wherein the loft angle of the club head or slug is between about 6° to about 20°.
8. The method of claim 1 , wherein β is about 1.222.