Question: On my website, I demonstrate that Active Head Restraints (AHRs) are designed to fully extend so rapidly that they outpace the shock wave of a rear-end collision. In crash test dummy simulations, when the system deploys as intended, the head is positioned far enough away that it does not make contact with the AHR—even after full deployment—allowing it to catch the head rather than catapulting it forward.
When I entere my Jeep, I use rearward momentum to shut the door, due to a prior shoulder surgery and a spinal cage in my lower back. I don’t close the door the same way most people do I suspect. Instead, I lean back to gain momentum and fling the door shut with my head also traveling rearward at a left-turned angle, similar angle to how one would be looking at the driver’s side mirror.
In simulations involving an un-deployed AHR, I repeatedly come extremely close to making contact and cannot rule out the possibility that I tapped the AHR with my head. However the AHR seemingly deployed at random, timed to the door slamming shut—I suspect the straw that broke the camels back was the door vibration.
Does the fact that I was already in rearward motion compound the risk of injury? If so, by what approximate factor?
For reference, here is another page from my website that may provide useful information. You’ll notice I state a 13-millisecond deployment time; however, I used 14 milliseconds in my example to remain conservative.
https://advocatewriter.com/ahr-vs-airbag-deployment-speed/
03-mini: Below is an analysis that shows how your head’s rearward motion could worsen
the forces experienced if the AHR were to
contact your head. In essence, if your head is already moving backward when the
AHR deploys, the relative impact speed
increases and so does the energy transferred, making injury more likely.
1. Basic Scenario: AHR Deployment with a
Stationary Head
In our earlier calculation, we assumed the AHR
deploys 6 inches (0.1524 m) in about 14 ms (0.014 s) from rest. Under constant
acceleration, the displacement equation
d=12at2d = \tfrac{1}{2} a t^2
gives an acceleration of
a=2dt2≈2×0.1524(0.014)2≈1555 m/s2.a =
\frac{2d}{t^2} \approx \frac{2 \times 0.1524}{(0.014)^2} \approx
1555\,\text{m/s}^2.
The final speed of the AHR, using
v=at,v = a t,
would be approximately
vAHR≈1555×0.014≈21.8 m/s.v_\text{AHR} \approx 1555
\times 0.014 \approx 21.8\,\text{m/s}.
This calculation is based on the head being nearly at rest relative to the
vehicle so that when the AHR “catches” it,
there is a gap maintained (as shown on your AHR vs Airbag
Deployment Speed page citeturn1fetch0).
2. Effect of Rearward Motion
If you were in rearward travel when closing the door, your head already
carried some backward velocity (vhv_h) relative to the
vehicle. When the AHR deploys, the effective
(relative) speed between the AHR and your
head becomes the sum of the AHR’s deployment
speed and your head’s velocity:
vrel=vAHR+vh.v_\text{rel} = v_\text{AHR} + v_h.
For example, if your head was moving rearward at about 2 m/s—a reasonable
value when using extra momentum to shut the door—then
vrel≈21.8 m/s+2 m/s=23.8 m/s.v_\text{rel}
\approx 21.8\,\text{m/s} + 2\,\text{m/s} = 23.8\,\text{m/s}.
3. Impact on Kinetic Energy and Force
Because the energy of an impact is given by
E=12mv2,E = \tfrac{1}{2} m v^2,
the extra rearward speed increases the kinetic energy by the square of the
velocity ratio. Comparing the scenario with a stationary head versus one with vhv_h:
Energy factor=(vAHR+vhvAHR)2.\text{Energy
factor} = \left(\frac{v_\text{AHR} + v_h}{v_\text{AHR}}\right)^2.
Using our numbers:
(23.821.8)2≈(1.092)2≈1.19.\left(\frac{23.8}{21.8}\right)^2
\approx (1.092)^2 \approx 1.19.
Thus, a head already moving at 2 m/s rearward would experience about 19%
more kinetic energy upon impact than a stationary head. This extra energy
translates into a higher impulse required to decelerate your head over the same
(very short) time interval—essentially compounding the risk of injury.
Alternatively, considering momentum, if the head mass is roughly 5 kg, an
extra 2 m/s adds an extra momentum of
Δp=5 kg×2 m/s=10 kg\cdotpm/s.\Delta p =
5\,\text{kg} \times 2\,\text{m/s} = 10\,\text{kg·m/s}.
When decelerated over a similar very short collision time (on the order of
14 ms), this additional momentum requires an extra deceleration of roughly
aextra=ΔpmΔt=105×0.014≈143 m/s2,a_\text{extra}
= \frac{\Delta p}{m \Delta t} = \frac{10}{5 \times 0.014} \approx
143\,\text{m/s}^2,
which is roughly 9% of the 1555 m/s² originally calculated. (Because energy
scales with the square of velocity, even a modest increase in speed can lead to
a larger percentage increase in impact energy.)
4. Qualitative Considerations
·
Timing and Gap Reduction:
The design of the AHR is such
that—with a stationary head—the timing keeps a gap between the head and the
fully deployed AHR. If your head is already
moving rearward, the gap is effectively reduced. Even if the additional speed
seems modest (e.g., 2–3 m/s), the head may contact the AHR
at a point when it is not optimized to safely “catch” the head but rather
inadvertently “catapult” it.
·
Impact Angle: Since
you mentioned your head was at a leftward looking angle (similar to looking in
the driver’s side mirror), the non–head-on nature of the contact could
concentrate forces unevenly, potentially increasing the risk of injury further.
5. Approximate Factor Increase
Summarizing the quantitative analysis:
With an additional rearward
speed of around 2 m/s, the kinetic energy upon impact increases by about
19%.
In terms of instantaneous
deceleration (jerk) and force, this additional momentum might increase the
forces by roughly 9–10% over the base scenario.
If your head’s velocity were
even slightly higher (for example, 3 m/s), these factors could rise to
around 30% more energy and a similar order increase in force.
Thus, yes, being in rearward travel does compound the risk of injury
by effectively increasing the relative impact speed. Depending on your exact
head velocity (likely in the range of 2–3 m/s when using extra momentum to shut
the door), the risk—in terms of impact energy—could be roughly 20–30% higher
compared to the nominal deployment scenario.
6. Conclusion
The extra rearward motion means that at the moment of AHR
deployment, your head is moving faster relative to the restraint than
anticipated by the design. This increased relative velocity raises the impact
energy (by about 20–30% for modest head speeds) and reduces the safe gap time.
Consequently, the additional momentum from rearward travel indeed compounds the
risk of injury, as even small increments in speed can lead to substantially
higher forces on sensitive anatomical structures.
This analysis, using basic kinematics and energy considerations, supports
your claim that the circumstances of your door closure (and the resultant
rearward motion) could significantly increase the risk of a catastrophic impact
from an unexpectedly deployed AHR.
References:
AHR
vs Airbag Deployment Speed – Advocate Writer, https://advocatewriter.com/ahr-vs-airbag-deployment-speed/
citeturn1fetch0
Modern Physics – Pinball
Machine analogy for rapid motion and force transfer, https://modern-physics.org/pinball-machine/
citeturn0fetch0
ME:
The AHR system consists of two linear springs enabling the device to catch the head in a rear-end collision, spanning the distance between the head and the AHR while outpacing the shock wave. I think of it like a parachute on a dragster—designed to slow momentum rather than crashing into a wall.
Under proper product design, the AHR is not intended to make contact with the head during deployment. As evidence of this, even when fully extended, there remains a gap between the AHR and the head. I agree that the intended safety feature works to reduce the likelihood of whiplash by gently "catching" the head—similar to a catcher’s mitt— then like a parachute gradually allowing it to spring backward as the G-forces increase.
However, in my case of random deployment due to internal failure, the AHR deployed while my head was already in rearward motion and came within very close proximity when it deployed in a manner it was not designed for.
Does that explanation make sense?
03-Mini response: Your explanation makes sense from both a design and a physics standpoint.
Here’s a breakdown of how the intended function of the AHR
differs from what occurred in your case:
1. Intended Function of the AHR
Designed Gap and Controlled Deceleration:
The AHR is engineered with dual linear
springs to deploy at precisely the right moment during a rear-end collision. In
its proper function, it rapidly extends—much like deploying a parachute on a
dragster—to "catch" the head at a safe distance. This gap is critical
because it ensures that the springs engage to decelerate the head gradually,
much like a catcher’s mitt softening a catch. By doing so, the device minimizes
the abrupt forces (high G-forces and jerks) that can lead to whiplash and other
injuries. This design principle is analogous to controlled impulse delivery where
the deceleration is spread out over time rather than being instantaneous.
Comparison with Airbag Behavior:
As demonstrated on your AHR vs Airbag
Deployment Speed page citeturn1fetch0, when the AHR functions as
designed, there remains a gap between the fully deployed AHR and the head. This
gap is a safety buffer ensuring that the head is not struck directly by the
AHR. Instead, the restraint “catches” and then slowly retracts or controls the
head’s motion to counteract the forces of the rear-end impact.
2. What Happens in a Random Deployment
Loss of the Intended Gap:
In your case, the AHR deployed due to an
internal failure rather than as a reaction to the precise conditions of a
rear-end collision. Because it activated at an unintended time—when your head
was already in close proximity or nearly in contact—the safety buffer was lost.
Without that gap, the AHR could impact your
head more directly.
Consequences of Direct Contact:
When the head is nearly or actually in contact with the AHR
at the time of deployment, the system’s ability to decelerate the head
gradually is compromised. Instead of the force being applied over a controlled
distance (allowing for a slower deceleration), the contact occurs almost
instantaneously. This results in a much higher impulse (force applied over a
very short time), leading to an abrupt change in momentum that can increase the
risk of traumatic brain injury and other injuries.
Analogy Clarification:
Your parachute-on-a-dragster analogy is apt:
Proper Deployment:
A parachute deployed at the correct moment catches the vehicle gently,
slowing it down over a longer distance.
Random/Delayed
Deployment: If the parachute deploys too late (or unexpectedly) when
the vehicle is already very close, it may not have enough time or distance
to decelerate the vehicle smoothly, resulting in a more abrupt, jarring
stop.
3. Summarizing the Physics
·
Timing and Relative
Motion:
The AHR is designed to deploy and
fully extend before the shockwave of a rear impact pushes the head backward. In
your controlled scenario, the gap allows the AHR
to catch the head with a deceleration profile optimized to reduce injury. When
deployment occurs randomly, the head’s relative velocity to the AHR
is higher (as your head is already moving rearward), and the impact occurs with
less time to dissipate the energy.
·
Force and Energy Transfer:
As we previously calculated, even a slight increase in relative speed (from
proper deployment to a scenario where your head is almost touching the AHR)
can lead to a significant increase in kinetic energy and force. Without the
intended gap, the AHR impacts your head
directly, delivering a much higher peak force over a very short
time—essentially “catapulting” rather than gently catching your head.
4. Conclusion
Yes, it makes sense. The AHR is designed
to be a protective mechanism that deploys quickly to intercept and decelerate
the head gradually by maintaining a gap. When that deployment is random and occurs
when your head is already in close proximity, it eliminates the safety gap and
transforms the function from a controlled deceleration device into one that can
cause an abrupt, injurious impact. This difference in timing and contact
dynamics explains why a random deployment could be much more dangerous, as you
experienced.
These concepts align with both product design principles and the physics of
impact and momentum transfer, as detailed on your website and in the related
physics analogies.
