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The Biomechanics of Impact Injury
Angular acceleration was implicated as a cause of brain injury, beginning with the theory by Holbourn (1943) and the extensive research conducted by Ommaya and Hirsch (1971), Ommaya et al. (1967), and Gennarelli et al. (1982). The concept of angular acceleration was proposed by Sir Isaac Newton in the 1680s (Newton’s Principia) where he laid down the laws of motion. However, Newton did not say how this quantity could be measured. In 2D, the measurement is accomplished by using a pair of linear accelerometers placed a known distance apart and facing the same direction (Mertz 1967). For 3D motion, many schemes have been proposed (see, e.g., Kane 1968). It turns out that all of the schemes can potentially yield unreliable results even though the equations used are sophisticated. In this chapter, the traditional method is first described and is shown to be numerically unstable. Then a different scheme is introduced to show that it is numerically stable but requires more sensors.
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5.1.
A reliable method for the measurement of angular acceleration, using linear accelerometers, was invented by:
[ ] (i)
Sir Isaac Newton
[ ] (ii)
Prof Kane at Stanford University
[ ] (iii)
Guy Nusholtz at the University of Michigan
[ ] (iv)
Researchers in biomechanics at Wayne State University
[ ] (v)
Researchers at the Naval Biodynamics Lab in New Orleans
5.2.
When using linear accelerometers to measure angular acceleration
[ ] (i)
It is better to use the 3222 configuration than the three triaxial configuration
[ ] (ii)
The accelerometers must have low crosstalk sensitivity
[ ] (iii)
The accelerometer calibration should not change with frequency content of the impact pulse
[ ] (iv)
A new sixaccelerometer method is now available without having to integrate the equations
[ ] (v)
All of the above
5.3.
The major difference between using 9 accelerometers in the 3222 configuration instead of the 6 accelerometers to measure angular acceleration is:
[ ] (i)
Minimization of error because the extra measurements can be used to check the computation
[ ] (ii)
The angular acceleration can be computed from algebraic instead of differential equations
[ ] (iii)
There is no accumulation of error during the computational process
[ ] (iv)
(i) and (iii)
[ ] (v)
(ii) and (iii)
5.4.
To verify an angular acceleration measurement, it is necessary to integrate the data twice to obtain angular displacement to compare this displacement with that measured by a different method, such as an optical method. The integration of
[ ] (i)
Angular acceleration to angular velocity cannot be done directly because angular velocity is noncommutative and special methods are needed to perform this integration
[ ] (ii)
Angular velocity to angular displacement cannot be done directly because angular displacement is noncommutative and special methods are needed to perform this integration
[ ] (iii)
Angular acceleration to angular velocity and that of angular velocity to angular displacement can be done directly because they are both commutative and no special methods are needed
[ ] (iv)
Angular velocity to angular displacement can be done directly because angular displacement is commutative and no special methods are needed to perform this integration
[ ] (v)
None of the above
5.5.
When angular acceleration is measured with only 6 accelerometers, the resulting equations in terms of the angular velocity components are nonlinear ordinary differential equations. Numerical solution of these nonlinear equations can result in instability of the computed angular acceleration because
[ ] (i)
The differential equations have unstable solutions
[ ] (ii)
The errors in measurement accumulate over time as the integration progresses
[ ] (iii)
The errors propagate because the numerical subroutine used to integrate the equations is unstable
[ ] (iv)
(i) and (iii)
[ ] (v)
None of the above
5.6.
The use of three triaxial accelerometers to measure angular acceleration is less reliable than the use of the 3222 configuration of linear accelerometers because
[ ] (i)
The triaxial method still requires integration of nonlinear differential equations
[ ] (ii)
The use of the three additional accelerometers in the triaxial configuration to check the computed angular acceleration from the other 6 accelerometers can still result in error accumulation
[ ] (iii)
It is not possible to align the triaxial accelerometers accurately
[ ] (iv)
(i) and (ii)
[ ] (v)
(i) and (iii)
5.7.
When linear accelerometers are used to measure angular acceleration, it is important that these transducers:
[ ] (i)
Have a steady zero baseline which does not drift with time
[ ] (ii)
Have low crosstalk sensitivity
[ ] (iii)
Respond linearly to increase in linear acceleration
[ ] (iv)
Have adequate frequency response to handle short duration impacts
[ ] (v)
All of the above
5.8.
An accurate and reliable alternate method of measuring angular acceleration is the:
[ ] (i)
Use of an angular accelerometer which yields this value directly
[ ] (ii)
Use of an angular velocity transducer and differentiating the data to yield angular acceleration
[ ] (iii)
Use of a highspeed video camera at 1000 frames per second and differentiating the angular displacement twice
[ ] (iv)
Use of intersecting laser techniques to obtain angular acceleration directly
[ ] (v)
None of the above
5.9.
Linear accelerometer manufacturers calibrate their accelerometers against a standard accelerometer using:
[ ] (i)
A shaker table
[ ] (ii)
Optical methods
[ ] (iii)
Rate table tests
[ ] (iv)
Drop tests
[ ] (v)
All of the above
5.10.
The major difference between using 9 accelerometers in the 3222 configuration instead of the 6 accelerometers to measure angular acceleration is:
[ ] (i)
Minimization of error because the extra measurements can be used to check the computation
[ ] (ii)
The angular acceleration can be computed from algebraic instead of differential equations
[ ] (iii)
There is no accumulation of error during the computational process
[ ] (iv)
(ii) and (iii)
[ ] (v)
(i) and (ii)
[ ] (i)
Sir Isaac Newton
[ ] (ii)
Prof Kane at Stanford University
[ ] (iii)
Guy Nusholtz at the University of Michigan
[ ] (iv)
Researchers in biomechanics at Wayne State University
[ ] (v)
Researchers at the Naval Biodynamics Lab in New Orleans
[ ] (i)
It is better to use the 3222 configuration than the three triaxial configuration
[ ] (ii)
The accelerometers must have low crosstalk sensitivity
[ ] (iii)
The accelerometer calibration should not change with frequency content of the impact pulse
[ ] (iv)
A new sixaccelerometer method is now available without having to integrate the equations
[ ] (v)
All of the above
[ ] (i)
Minimization of error because the extra measurements can be used to check the computation
[ ] (ii)
The angular acceleration can be computed from algebraic instead of differential equations
[ ] (iii)
There is no accumulation of error during the computational process
[ ] (iv)
(i) and (iii)
[ ] (v)
(ii) and (iii)
[ ] (i)
Angular acceleration to angular velocity cannot be done directly because angular velocity is noncommutative and special methods are needed to perform this integration
[ ] (ii)
Angular velocity to angular displacement cannot be done directly because angular displacement is noncommutative and special methods are needed to perform this integration
[ ] (iii)
Angular acceleration to angular velocity and that of angular velocity to angular displacement can be done directly because they are both commutative and no special methods are needed
[ ] (iv)
Angular velocity to angular displacement can be done directly because angular displacement is commutative and no special methods are needed to perform this integration
[ ] (v)
None of the above
[ ] (i)
The differential equations have unstable solutions
[ ] (ii)
The errors in measurement accumulate over time as the integration progresses
[ ] (iii)
The errors propagate because the numerical subroutine used to integrate the equations is unstable
[ ] (iv)
(i) and (iii)
[ ] (v)
None of the above
[ ] (i)
The triaxial method still requires integration of nonlinear differential equations
[ ] (ii)
The use of the three additional accelerometers in the triaxial configuration to check the computed angular acceleration from the other 6 accelerometers can still result in error accumulation
[ ] (iii)
It is not possible to align the triaxial accelerometers accurately
[ ] (iv)
(i) and (ii)
[ ] (v)
(i) and (iii)
[ ] (i)
Have a steady zero baseline which does not drift with time
[ ] (ii)
Have low crosstalk sensitivity
[ ] (iii)
Respond linearly to increase in linear acceleration
[ ] (iv)
Have adequate frequency response to handle short duration impacts
[ ] (v)
All of the above
[ ] (i)
Use of an angular accelerometer which yields this value directly
[ ] (ii)
Use of an angular velocity transducer and differentiating the data to yield angular acceleration
[ ] (iii)
Use of a highspeed video camera at 1000 frames per second and differentiating the angular displacement twice
[ ] (iv)
Use of intersecting laser techniques to obtain angular acceleration directly
[ ] (v)
None of the above
[ ] (i)
A shaker table
[ ] (ii)
Optical methods
[ ] (iii)
Rate table tests
[ ] (iv)
Drop tests
[ ] (v)
All of the above
[ ] (i)
Minimization of error because the extra measurements can be used to check the computation
[ ] (ii)
The angular acceleration can be computed from algebraic instead of differential equations
[ ] (iii)
There is no accumulation of error during the computational process
[ ] (iv)
(ii) and (iii)
[ ] (v)
(i) and (ii)
Prob

Ans


1

(iv)

2

(v)

3

(v)

4

(ii)

5

(ii)

6

(iv)

7

(v)

8

(i)

9

(i)

10

(iv)

P.C. Begeman, J. Kopacz, W.N. Hardy, R.S. Levine, A.I. King, Strains and forces in the human medial collateral ligament during lateral impacts, in
1987 ASME Applied Mechanics Bioengineering, and Fluids Engineering Conference, vol 84, ASME, AMD, New York, 1987, pp. 233–236
J.E. Bortz, A new concept in strapdown inertial navigation, in Technical Report No. NASATRR329, National Aeronautics and Space Administration, Washington, DC, 1970
M. Franklyn, B. Fildes, L. Zhang, K. Yang, L. Sparke, Analysis of finite element models for head injury investigation: reconstruction of four real world impacts. Stapp Car Crash J.
49, 1–32 (2005)
T. Gennarelli, L. Thibault, J. Adams, D. Graham, C. Thompson, R. Marcincin, Diffuse axonal injury and traumatic coma in the primate. Ann. Neurol.
12, 564–574 (1982)
CrossRef
A. Holbourn, Mechanics of head injuries. Lancet
242(6267), 438–441 (1943)
CrossRef
T.R. Kane,
Dynamics (Holt, Rinehart and Winston Inc, New York, 1968)
MATH
H.J. Mertz, Kinematics and Kinetics of Whiplash, PhD Dissertation
, Wayne State University, Detroit, MI, 1967
N. Mital, A. King, Computation of rigidbody rotation in threedimensional space from bodyfixed linear acceleration measurements. J. Appl. Mech.
46(4), 925–930 (1979)
CrossRef
N. Mital, Computation of rigidbody rotation in threedimensional space from bodyfixed acceleration measurements, PhD Dissertation, Wayne State University, Detroit, MI, 1978
J. Morris, Accelerometry—a technique for the measurement of human body movements. J. Biomech.
6(6), 729–736 (1973)
CrossRef
G.S. Nusholtz, P.S. Kaiker, R.J. Lehman, Critical limitations on significant factors in head injury research, in
30th Stapp Car Crash Conference, San Diego, CA, 1986
A. Ommaya, A. Hirsch, Tolerances for cerebral concussion from head impact and whiplash in primates. J. Biomech.
4(1), 13–21 (1971)
CrossRef
A.K. Ommaya, P. Yarnell, A.E. Hirsch, E.H. Harris, Scaling of experimental data on cerebral concussion in subhuman primates to concussion threshold for man, in
11th the Stapp Car Crash Conference, SAE Paper No. 670906, Anaheim, CA, 1967
A.J. Padgaonkar, K. Krieger, A. King, Measurement of angular acceleration of a rigid body using linear accelerometers. J. Appl. Mech.
42(3), 552–556 (1975)
CrossRef
C.W. Tan, S. Park, K. Mostov, P. Varaiya, Design of gyroscopefree navigation systems, in
2001 IEEE, Intelligent Transportation Systems (2001)
G. Teasdale, B. Jennett, Assessment of coma and impaired consciousness – a practical scale. Lancet
304(7872), 81–84 (1974)
CrossRef
 Titel
 Measurement of Angular Acceleration
 DOI
 https://doi.org/10.1007/9783319497921_5
 Autor:

Albert I. King
 Sequenznummer
 5
 Kapitelnummer
 Chapter 5