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International Journal of Crashworthiness

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Physical and empirical models for motorcycle speed

estimation from crush
a a ab c
Denis P. Wood , Colin Glynn , Conor O’Dea & Darren Walsh
a
Denis Wood Associates, Isoldes Tower, Dublin, Ireland
b
School of Engineering, Trinity College Dublin, Ireland
c
Dr JH Burgoyne & Partners LLP, Hertfordshire, UK
Published online: 22 May 2014.

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To cite this article: Denis P. Wood, Colin Glynn, Conor O’Dea & Darren Walsh (2014) Physical and empirical
models for motorcycle speed estimation from crush, International Journal of Crashworthiness, 19:5, 540-554, DOI:
10.1080/13588265.2014.918300

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 International Journal of Crashworthiness, 2014
Vol. 19, No. 5, 540
554, http://dx.doi.org/10.1080/13588265.2014.918300

Physical and empirical models for motorcycle speed estimation from crush
Denis P. Wooda, Colin Glynna*, Conor O’Deaa,b and Darren Walshc
a
Denis Wood Associates, Isoldes Tower, Dublin, Ireland; bSchool of Engineering, Trinity College Dublin, Ireland; cDr JH Burgoyne &
Partners LLP, Hertfordshire, UK
(Received 1 November 2013; accepted 23 April 2014)

This paper presents a new physical model for estimating motorcycle speed in motorcycle to car collisions from the
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motorcycle wheelbase reduction and car deformation depth. This model combines previously published specific energy
characteristics of motorcycles and scooters derived from barrier tests with a motorcycle to car interface Force
Balance
approach to estimate the collision energy absorbed by the car. This Force
Balance approach and three previously
published models for motorcycle speed estimation are compared using a data-set of 107 published staged collisions, over a
collision speed range of 30
122 kph. The Force
Balance model and a previously published empirical model were shown
to compare well with the available staged tests, with statistically insignificant mean residuals of 0.8 and 0.7 kph for the
predicated speed when compared with actual speeds. The corresponding standard errors were 10.3 and 11.2 kph,
respectively. Two other previously published physical models were shown to significantly under-predict speed, with mean
residuals of 5.6 and 19.5 kph, respectively, with corresponding standard errors of 9.5 and 11.8 kph. An analysis of impacts
into hard and soft areas of the car sides show that the presented Force
Balance model is robust when applied to both soft
and hard impact locations, while the empirical approach is shown to be robust for soft impact locations but under-predicts
collision speed by a mean of 3 kph for hard impact locations.
Keywords: motorcycle/scooter collisions; speed estimation; car deformation; motorcycle; wheelbase deformation; wheel-
base shortening

1. Introduction collision energy absorbed by the car, Searle’s [18] linear

Estimation of collision speed is an important aspect in the force model and an empirical model derived by Schmidt
reconstruction of impacts between motorcycles and cars [17]. The comparison uses the results of 107 published
and has applications in biomechanical injury research as staged tests where motorcycles and scooters are impacted
well as litigation. Barrier impact tests by Severy [19], in against stationary (N ¼ 100) and moving (N ¼ 7) cars. In
the 1960s, indicated that impact speed was related to the original Wood [25], Searle [18] and Schmidt [17]
motorcycle wheelbase shortening. Since then a number of models a number of the staged tests were used for model
researchers, including Limpert [12] and Schmidt [17] derivation and hence not available for validation/compari-
have proposed empirical relations between impact speed son purposes.
and either motorcycle wheelbase shortening or the combi-
nation of wheelbase shortening and the crush depth of the 2. Theory
car. More recently, Wood [24,25] and Searle [18] pro-
The notation used is detailed in Appendix 1.
posed physical models based on the proposition that struc-
It is well established that
tural deformation and energy absorption behaviour of
 1
motorcycles are proportional to the motorcycle mass. This 2Et 2
concept, originally proposed by Pugsley and Macaulay Vccs ¼ ; ð1Þ
Moa
[16] in relation to railway coaches, has been shown by
Wood [22,23] to apply to the frontal crush properties of where Vccs is the collision closing speed, i.e. the relative
cars. This paper extends previous work by Wood [24,25] speed of approach of the vehicles towards each other. In
with the introduction of a ‘Force
Balance’ approach this paper, the Vccs is the relative velocity along the longi-
between the motorcycle and car to estimate the proportion tudinal axis of the motorcycle.
of the collision energy absorbed by the struck car. This And where
‘Force
Balance’ model is compared to the original Wood
model [25] which uses an empirical estimate of the Et ¼ Em=c þ Ecar : ð2Þ

*Corresponding author. Email: colin@deniswood.com

Ó 2014 Taylor & Francis

 International Journal of Crashworthiness 541

And Moa is the overall equivalent mass of the colliding types in Table A2. The scooter specific energy character-
pair as detailed in the following: istics bounded those of the motorcycles. Statistical cross-
comparison between the scooter and motorcycle data
Mm=c Mcar showed that they could be treated as a common
Moa ¼ : ð3Þ
Mm=c þ Mcar population.
By comparison, Searle [18] obtained the relation for
For impacts offset from the centre of gravity of the car specific energy of
the effective mass of the car, derived from the offset of
the line of action of the motorcycle velocity vector, is SE ¼ 703dw2 : ð8Þ
used.
This is based on a linear force
deflection model for
 
k2 motorcycle wheelbase deformation and is derived from a
Mcar;eff ¼ Mcar ; ð4Þ combination of barrier (N ¼ 13) and motorcycle to car
ðk 2 þ h2 Þ
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tests (N ¼ 44) [18].

where h is the offset of the line of action of the motorcy- In [25], Wood carried out an empirical analysis of the
cle/scooter velocity vector and k is the car’s radius of energy absorbed by the sides of the cars and obtained the
gyration, which can be estimated for cars from Wood relation,
[21]:
Ecar ¼ 65; 305ðdcar
0:058Þ; ð9Þ
0:931 2
k2 ¼ ðl þ w2 Þ ð5Þ
12 where dcar is the residual penetration depth, measured in
metres, perpendicular to the side of the car and dcar is
and where l and w are the length and width of the car, more than 0.058 metres.
respectively. For the motorcycle population, An alternative approach to estimate the proportion of
collision energy absorbed by the car is to rely on the fact
Em=c that during the impact the motorcycle and car experience
Specific energyðSEÞ ¼ ; ð6Þ
Mm=c equal but opposite interface forces. Wood [25] has shown
with similar force deformation profiles for the motorcycle
where SE is the specific energy (Nm/kg) absorbed by the and car that
motorcycle/scooter and Mm=c is the kerb mass of the
motorcycle/scooter. dcar
Ecar ¼ Em=c : ð10Þ
Recovery and restitution effects can be ignored when dw
the total collision energy absorbed during the impact (i.e.
the energy absorbed to maximum dynamic crush) is corre- This is a ‘Force
Balance’ approach to obtain the
lated to the wheelbase shortening of the motorcycle and/or energy absorbed by the car. The vehicle deformations in
the penetration depth of the car. Equation (10) comprise the maximum deformations dur-
From analysis of barrier impact tests (N ¼ 43) of ing the impact, rather than the residual deformations after
motorcycles (N ¼ 18) and scooters (N ¼ 25), Wood [25] the collision has occurred.
has shown that

3. Alternative models
SE ¼ 641:7ðdw þ 0:1Þ1:89 ; ð7Þ
3.1. Wood original model [25]
where dw ¼ average residual wheelbase shortening of This approach uses Equations (1)
(4) in combination
motorcycle/scooter, obtained from the average residual with the specific energy relation for motorcycles and
wheelbase of the deformed motorcycle/scooter and scooters derived from barrier test data, Equation (7) and
knowledge of the un-deformed wheelbase length. the empirical equation for car energy, Equation (9), to
The barrier test data used by Wood [25] to derive the estimate collision closing speed.
population specific energy characteristics includes eight
types of scooter and six types of motorcycle, produced
between the early 1980s and the present day. The motor- 3.2. Searle model [18]
cycles and scooters used are detailed in Table A2 of The Searle model is based on linear force deformation of
Appendix 2. the motorcycle fork assembly, Equation (8) and a
Individual specific energy characteristics were derived ‘force
balance’ approach for car energy estimation. In
for the first four scooter types and the first two motorcycle conjunction with Equations (1)
(4) this yields a collision
 542 D.P. Wood et al.

Table 1. Model independent data-sets. closing speed as

Model Independent data-set   12
Mm=c 0:89
Wood Original 76 Vccs ¼ 1283:4 ðdw þ 0:1Þ ðdw þ dcar þ 0:15Þ :
Moa
Searle 63
Empirical 87 ð13Þ
Force
Balance 107
A complete derivation of Equation (13) is shown in
Appendix 3. The above equations are in S.I. units with
mass in kg, length in metres and speed in m/s.
closing speed relation as follows:

 12 4. Comparison
Mm=c
Vccs ¼ ð1406Þðdw þ dcar Þðdw Þ : ð11Þ
The different models can be compared in two ways. First,
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Moa
each approach can be applied to all independent staged
test data available for the respective models from the
3.3. Schmidt Empirical model [17] available set of 107 staged tests, with those staged tests
The empirical model for estimation of collision closing used for model development excluded. The 107 staged
speed derived by Schmidt [17] is tests were carried out and published by various research-
ers, see Table A4 of Appendix 4 for details. The second
Vccs ¼ 7:02 þ 35:52dw þ 15:5dcar : ð12Þ approach is to use a common subset of independent staged
tests. The common subsets are those tests which were not
used in the development of any of the compared models.
3.4. Force
Balance model This approach is used to compare the Searle, Schmidt and
From Equations (1)
(7) and (10), including offset, the ‘Force
Balance’ models. The available data-sets are
‘Force
Balance’ model yields the estimation for collision detailed in Table 1 while Table 2 sets out the range of

Table 2. Data-set parameter comparison.

Data-set Wood Original 76 Schmidt 87 Searle 63 Force
Balance 107

No. of motorcycles 74 (97%) 77 (88%) 54 (86%) 96 (90%)

No. of scooters 2 (3%) 10 (11%) 9 (14%) 11 (10%)
M/c to car impact at 90 67 78 54 98
M/c to car impact not at 90 9 9 9 9
Impacts to stationary car 69 80 67 100
Impacts to moving car 7 7 7 7
Hard collisions 27 (36%) 27 (31%) 21 (33%) 34 (32%)
Soft collisions 49 (64%) 60 (69%) 42 (67%) 73 (68%)
Min M/c mass (kg) 115 74.5 74.5 74.5
Mean M/c mass (kg) 209 195 186 204
Max M/c mass (kg) 329 304 304 329
Min car mass (kg) 594 594 594 594
Mean car mass (kg) 1110 1181 1158 1173
Max car mass (kg) 1646.5 1769 1769 1769
Ratio of M/c to car mass 1:5.3 1:6.1 1:6.2 1:5.8
Min M/c WB reduction (m) 0.09 0.08 0.09 0.08
Mean M/c WB reduction (m) 0.25 0.25 0.25 0.25
Max M/c WB reduction (m) 0.48 0.48 0.43 0.48
Min car deformation (m) 0.038 0.038 0.038 0.038
Mean car deformation (m) 0.31 0.32 0.29 0.3
Max car deformation (m) 0.9 0.9 0.76 0.9
Min Vccs actual (kph) 39 30 30 30
Mean Vccs actual (kph) 77.1 75.2 73.6 73.8
Max Vccs actual (kph) 122 122 116.2 122
 International Journal of Crashworthiness 543

Table 3. Independent data results.

Independent data for each model Wood Original Schmidt Empirical Searle Force
Balance

N 76 87 63 107
Mean residual 4.95 0.65 19.17 0.77
SE of residual 9.49 11.22 11.79 10.25
t 4.55 0.54 12.91 0.78
Regression of residuals Intercept 11.22 0.68 24.75 4.15
Slope
0.09 0.00
0.10
0.05
r2 0.030 0.000 0.028 0.007

parameter values (motorcycle mass, impact speed, etc.) distribution of collisions classified as hard or soft is
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for each of the four models. 64%
69% soft and 31%
36% hard, and provide a fair
It is apparent from Table 2 that a majority of the comparison between each of the models in this regard.
parameters listed show relatively similar values across the The percentage of staged tests in each of the data-sets
respective data-sets. The mean mass of the motorcycles involving scooters instead of motorcycles is varied, rang-
ranges from 186
209 kg with an overall minimum and ing from 3% to 14%. However, it was shown in [25] that
maximum of 74.5 and 329 kg, respectively. The mean motorcycles and scooters can be regarded as a common
mass of the cars ranges from 1110
1181 kg with an over- population when considered in specific energy terms.
all minimum and maximum of 594 and 1769 kg, respec-
tively. This results in similar mean ratio of the mass of the
motorcycle to the mass of the car at 1:5.3 to 1:6.2. The 4.1. Independent data-sets
mean wheelbase reductions are the same for each subset Table 3 shows the results for each model where all inde-
at 0.25 m with an overall minimum and maximum of 0.08 pendent staged data available for each model are used, i.e.
and 0.48 m, respectively. The mean car deformation is in all data from the 107 staged tests, which were not used in
a comparably tight range of 0.29
0.31 m with an overall the particular model development. Figures 1
4 show the
minimum and maximum of 0.038 and 0.9 m, respectively. comparison between actual collision closing speed, Va ,
The range of closing speed, Vccs , varies from an overall and predicted collision closing speed, Vp . Note that the
minimum of 30 kph to a maximum of 122 kph. The speeds shown in all the figures are in kph.

Figure 1. Wood Original model, 76 independent data, V actual vs. V predicted.

 544 D.P. Wood et al.
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Figure 2. Schmidt Empirical model, 87 independent data, V actual vs. V predicted.

Regression of the residuals, Va
Vp , against Vp, both approaches under-predict the actual collision closing
shows that the distributions are independent of speed. The speed (in almost all cases for the Searle model). For both
range of standard error values is 9.5
11.8 kph. Chi-square the Schmidt Empirical model and the ‘Force
Balance’
tests show no significant difference between standard model, the mean residuals of 0.65 and 0.77 kph are not
errors. The mean residuals for the Searle model, 19.1 kph, statistically significant with t values of 0.54 (P ¼ 59%)
and Wood Original model, 5 kph, show that on average and 0.78 (P ¼ 44%), respectively.

Figure 3. Searle model, 63 independent data, V actual vs. V predicted.

 International Journal of Crashworthiness 545
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Figure 4. Force
Balance model, 107 independent data, V actual vs. V predicted.

4.2. Common 63-test data-set 4.3. Common 87-test data-set

The Schmidt Empirical and the ‘Force
Balance’ The ‘Force
Balance’ and Schmidt Empirical approaches
approaches are directly compared with the Searle can also be directly compared with each other using their
approach by using their common data-set of 63 staged common data-set of 87 staged tests (tests used in neither
tests (tests not used in any of the three model develop- model development). Table 5 shows the comparison of
ments). Table 4 shows the comparison between the results between the approaches. The mean residual for the
approaches while Figures 5 and 6 compare actual collision ‘Force
Balance’ data is 1.1 kph, which is an increase
closing speed, Va , with predicted collision closing speed, compared to that of the 107 staged tests while standard
Vp , for the Schmidt Empirical and the ‘Force
Balance’ error remains almost the same at 10.5 kph.
approaches, respectively. The standard error in both cases
is seen to increase slightly. The mean residuals of the
5. Discussion
Schmidt and ‘Force
Balance’ data are 0.8 and 0.3 kph,
respectively. These compare with a mean residual of 19.2 Comparison with all available staged tests shows that the
kph for the Searle approach. Schmidt Empirical model (N ¼ 87) and the newly pre-
sented ‘Force
Balance’ model (N ¼ 107) have mean

Table 4. Searle, Schmidt Empirical and Force
Balance mod- Table 5. Schmidt Empirical and Force
Balance models, 87
els, 63 common data results. common data results.

Schmidt Force
Schmidt Force

Independent Searle data Searle Empirical Balance Independent data for each model Empirical Balance

N 63 63 63 N 87 87
Mean residual 19.17 0.77 0.29 Mean residual 0.65 1.1
SE of residual 11.79 12.26 11.18 SE of residual 11.22 10.46
t 12.91 0.50 0.21 t 0.54 0.98
Regression of residuals Intercept 24.75 0.02 4.56 Regression of residuals Intercept 0.68 4.32
Slope
0.10 0.01
0.06 Slope 0.00
0.04
r2 0.028 0.000 0.010 r2 0.000 0.007
 546 D.P. Wood et al.
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Figure 5. Schmidt Empirical model, 63 independent Searle data, V actual vs. V predicted.

under-predictions of 0.65 and 0.77 kph, respectively. compared to their available staged tests, with mean under-
Their corresponding t-values are 0.54 (P ¼ 59%) and 0.78 predictions of 19.2 and 5 kph, respectively. The Wood
(P ¼ 44%) which are not statistically different from zero. Original model [25] was originally validated using 13
However, the Searle and Wood Original approaches independent staged tests with a mean residual of 2.5 kph,
have been shown to under-predict collision speed when a standard deviation of 11.5 kph and a statistically

Figure 6. Force
Balance model, 63 independent Searle data, V actual vs. V predicted.

 International Journal of Crashworthiness 547

Table 6. Hard/soft data comparison, Schmidt Empirical and Force
Balance models.

Independent soft/hard data Schmidt Empirical soft Force
Balance soft Schmidt Empirical hard Force
Balance hard

N 60 73 27 34
Mean residual
0.40 0.62 3.00 1.09
SE of residual 10.18 9.73 13.17 11.33
t
0.30 0.54 1.18 0.56
Regression of residuals Intercept
4.47
0.43 9.09 10.45
Slope 0.05 0.01
0.08
0.13
r2 0.01 0.00 0.018 0.062

insignificant t-value of 0.77 (P ¼ 46%). When the Wood and shows that the distribution is ‘normal’. In all of the
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Original model is applied to the larger independent 76 comparisons, the standard error for the ‘Force
Balance’
data-set the mean residual increases to 5 kph while the approach is less than that obtained for the Schmidt model
standard error shows a decrease to 9.5 kph, with a statisti- (11.2 kph versus 12.3 kph for the 63 Searle data-sets, and
cally significant t-value of 4.55 (P ¼ 0%). 10.5 kph versus 11.2 kph for the 87 Schmidt data-sets).
Comparison between actual collision closing speed, An explanation for the difference is that the Schmidt
Va , and predicted collision closing speed, Vp , for all four model does not take into account the influence of variation
approaches shows that the trend of Va against Vp can be in the motorcycle/scooter and car masses. When the
considered to be 1:1. This is confirmed by the regression ‘Force
Balance’ model is applied to the data-sets with
of residuals Va
Vp against Vp with the extremely low the mass component excluded from Equation (13) the
regression coefficients, r2 , detailed in Table 2. This shows standard error increases (12.5 kph for the 63 Searle data-
that the distributions of residuals for all four approaches sets, and 11.5 kph for the 87 Schmidt data-sets) when
can be considered to be independent of speed over the pre- compared to Equation (13) where the mass effect is
dicted Vp range for the Va range of 30
122 kph. included. The scatter in the data reflects the range of vari-
The standard errors for all four approaches are similar, ation in the structural characteristics of the motorcycle/
with the Wood Original and ‘Force
Balance’ approaches scooter and car populations with structurally ‘soft’
having the lowest values. Figure 7 shows the cumulative vehicles resulting in over-prediction of collision speed
distribution of residuals for the ‘Force
Balance’ model and under-prediction for structurally ‘hard’ vehicles.

Figure 7. Cumulative distribution of Force
Balance using 107 independent data compared with normality.
 548 D.P. Wood et al.

5.1. Car ‘hard’ and ‘soft’ structures However, this is within the 95% confidence range of
It is common case that the structural characteristics of the 9.8
13.2 kph for the standard error of 11.2 kph. The
sides of cars vary along the length of the cars. The struc- ‘hard’ data yields a mean residual of 3 kph with a corre-
turally ‘hard’ areas are typically: sponding t ¼ 1.18 (P ¼ 24%). These results indicate that
the Schmidt Empirical model is very robust when applied
(1) the wheels; to soft data but when applied to ‘hard’ data, i.e., ‘hard’
(2) the A, B or C pillar; impact locations on the sides of cars, results in a mean
(3) the firewall-front bulkhead. under-prediction of the collision speed of 3 kph.
For the ‘Force
Balance’ model the ‘soft’ data yields a
Wood [24] using the Wood Original [25] approach mean residual of 0.6 kph, with a t ¼ 0.54 (P ¼ 59%) while
found that impacts against the ‘hard’ portions of the car the ‘hard’ data yields a mean residual of 1.1 kph with t ¼
sides resulted in significant under-prediction of collision 0.56 (P ¼ 58%). The standard errors of 9.7 and 11.3 kph
speed by 10%. are close to the overall data-set value of 10.3 kph and
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For the available data-sets of staged collisions (87 for within the 95% confidence range of 9.0
11.8 kph. The
Schmidt Empirical and 107 for Force
Balance) the distri- similarity in the mean residual, standard error and t-values
bution of collisions classified as hard or soft is 68%
69% for the ‘Force
Balance’ model when applied to either the
soft and 31%
32% hard, and provide a fair comparison soft or hard data indicates that this model provides a
between these two models in this regard. robust prediction of collision speed regardless of whether
Table 6 shows the results for both the Schmidt Empiri- the impact is at a structurally soft or hard location on the
cal and ‘Force
Balance’ models when applied to their car. This is explained by the manner of the physical model
independent hard/soft data while Figures 8 and 9 show the used where an increase in motorcycle wheelbase deforma-
comparison between actual collision closing speed, Va , tion due to impacting a ‘hard’ area of a car yields an
and predicted collision closing speed, Vp , for Schmidt increase in the contribution of motorcycle deformation to
‘hard’ and ‘Force
Balance’ ‘soft’ impact areas, respec- the speed estimation, refer to Equation (13).
tively. For the Schmidt Empirical model, the ‘soft’ data
yields mean residual of
0.4 kph, which shows a slight
over-prediction when compared to both the 63 Searle and 5.2. Angled collisions
87 independent results. The database of 107 published staged collisions includes 9
For the Schmidt Empirical model with the ‘hard’ data angled collisions and 98 broadside (90 ) collisions, see
the standard error is seen to increase to 13.2 kph. Table A4 of Appendix 4. The angled collisions were

Figure 8. Schmidt Empirical model, 27 independent hard data, V actual vs. V predicted.
 International Journal of Crashworthiness 549
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Figure 9. Force
Balance model, 73 independent soft data, V actual vs. V predicted.

within 45 of the broadside collision, i.e. a collision angle with 1.47 kph) or standard error (10.3 kph compared with
range of 45
135 , as shown in Figure A4 of Appendix 4. 11.1 kph) with a t-test value of 0.21 (t-critical ¼ 2.26) and
A comparison of the 90 and angled collisions for the an F-value of 0.05 (F-critical ¼ 3.93).
Force
Balance model shows no statistically significant Figure 10 shows the comparison between actual colli-
difference in either the mean residual (0.66 kph compared sion closing speed, Va , and predicted collision closing

Figure 10. Force
Balance model, nine angled collisions, V actual vs. V predicted.
 550 D.P. Wood et al.

speed, Vp , for the nine angled collisions using the Force- locations but to have under-predicted by a mean value of

Balance model together with the 1:1 line. 3 kph for hard impact locations.
In conclusion, both the ‘Force
Balance’ and Schmidt
Empirical approaches are shown to predict collision clos-
6. Conclusion ing speed from motorcycle/scooter wheelbase deforma-
This paper compares four approaches to the estimation of tion and car body deformation over the speed range of
motorcycle collision speed from motorcycle/scooter and 30
122 kph with standard errors of 10.3 and 11.2 kph,
car deformation. Three approaches, Wood [25], Schmidt respectively. The Schmidt empirical model has the merit
[17] and Searle [18], have been previously published but of being simple in application. The ‘Force
Balance’
either without comparison with independent data, Searle model has the merit of being based on a physical represen-
[18], or comparison with small data-sets, Wood [25] (N ¼ tation and being able to accommodate variation in vehicle
13) and Schmidt [17] by Bartlett [2] (N ¼ 25). Here, a masses.
database of up to 107 published staged tests is used. When applying the Force
Balance approach to indi-
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The new model set out in this paper applies the princi- vidual collisions a number of factors need to be taken into
ple of ‘Force
Balance’ at the interface between the account. There must be clear penetration of the front
motorcycle/scooter and car to estimate the collision wheel of the motorcycle/scooter into the side of the car.
energy absorbed by the car. This ‘Force
Balance’ is com- The collision angle of the motorcycle/scooter into the car
bined with previously published (Wood [25]) specific must be within 45 of a broadside impact. The front forks
energy characteristics for motorcycles and scooters. This and assembly, while deformed, must be intact and not
model is compared against the 107 staged test database. fractured or broken away.
A comparison of each of the models with the available
staged tests show that the ‘Force
Balance’ model and the References
Schmidt [17] empirical model both demonstrate a good [1] K.S. Adamson, P. Alexander, E.L. Robinson, G.M.
comparison with the data. Wood Original [25] and Searle Johnson, C.I. Burkehead, J. McManus, G.C. Anderson,
[18] are shown to significantly under-predict impact speed R. Aronberg, J.R. Kinney, and D.W. Sallmann, 17 motor-
when compared with the available data. The cycle crash tests into vehicles and barriers, SAE paper
‘Force
Balance’ model and the Schmidt Empirical model 2002-01-055, 2002.
[2] W. Bartlett, B. Focha, and C. Kauderer, 25 moving motor-
have mean residuals of 0.8 and 0.7 kph and standard errors cycle into stationary car tests: CA2RS 2009 data, July/
of 10.3 and 11.2 kph, respectively. With t-values of 0.78 August 2013, test carried out in Sonomoma County Air-
and 0.54 the mean residuals are shown to be statistically port, Santa Rosa, CA, 2009.
insignificant. The Wood Original [25] and Searle [18] had [3] V. Craig, Compiles for motorcycle/auto crash test results,
mean residuals of 5.0 and 19.2 kph and reflect the signifi- November/December, 2012, tests conducted by the Uni-
versity of Tulsa Consortium, hosted by New York State-
cant under-prediction of collision speed. wide Traffic Accident Reconstruction Society, 2012.
A common subset of 63 staged tests from the total 107 [4] V. Craig, Motorcycle/van high-speed crash test, Accident
database not used in the development of any of the Investigation Q, 51(summer) (2008), pp. 26
27.
‘Force
Balance’, Schmidt, and Searle models were used [5] CTS crashtest-service.com, Test 10402, 1994. Available at
to compare the three. The mean residuals of 0.8, 0.3 and http://www.crashtest-service.com/WEB_GB/start.asp.
[6] CTS crashtest-service.com, Test 11374, 1995. Available at
19.2 kph, respectively, highlight the degree of under-pre- http://www.crashtest-service.com/WEB_GB/start.asp.
diction in the Searle model relative to the other [7] CTS crashtest-service.com, Test 11382, 1995. Available at
approaches. The t-values are 0.21 (P ¼ 83%), 0.51 (P ¼ http://www.crashtest-service.com/WEB_GB/start.asp.
61%) and 12.91 (P ¼ 0%), respectively. This shows that [8] CTS crashtest-service.com, Test 14613 (test carried out by
while mean residual of the ‘Force
Balance’ and Schmidt J. Priester and M. Weyde), 2005. Available at http://www.
crashtest-service.com/WEB_GB/start.asp.
model are statistically insignificant, the mean residual of [9] CTS crashtest-service.com, Test 16225 (test carried out by
the Searle model is not so. J. Priester and M. Weyde), 2008. Available at http://www.
A common subset of 87 staged tests was used to fur- crashtest-service.com/WEB_GB/start.asp.
ther compare the ‘Force
Balance’ and Schmidt [10] CTS crashtest-service.com, Test 16226 (test carried out by
approaches. The mean residuals are 1.1 and 0.7 kph, J. Priester and M. Weyde), 2008. Available at http://www.
crashtest-service.com/WEB_GB/start.asp.
respectively, which with t-values of 0.98 (P ¼ 33%) and [11] G.K. Kasanicky, P. Kohut, and J. Priester, Analysis of Sin-
0.54 (P ¼ 59%) are statistically insignificant. However, gle-Track Vehicle Accidents, Zilina University Publishers,
the under-prediction by the ‘Force
Balance’ model is Zilina, 2003.
higher, on average, than the Schmidt model by 0.4 kph. [12] R. Limpert, Motor Vehicle Accident Reconstruction and
The sides of cars have structurally ‘hard’ and ‘soft’ Cause Analysis, 5th ed., Michie Pub, Charlottesville,
VA, 1994.
areas. The ‘Force
Balance’ model is robust for both hard [13] J. Priester and M. Weyde, Tests carried out in 2005. CD-
and soft impact locations while the Schmidt [17] empiri- ROM, Ingenieur- und Kfz Sachverstandigenburo Priester
cal model is shown to have been robust for soft impact und Weyde, Saarbr€ ucken, Berlin, 2005.
 International Journal of Crashworthiness 551

[14] J. Priester and M. Weyde, Tests carried out in Berlin in SE ¼ specific energy (Nm/kg)
July and September 2000. CD-ROM, Ingenieur-und Kfz- t ¼ t-test value
Sachverstandigenburo Priester und Weyde, Saarbr€ ucken, V ¼ speed (m/s)
Berlin, 2000. w ¼ width of car (m)
[15] J. Priester and M. Weyde, Tests carried out in May 2004,
Eindhoven. CD-ROM, Ingenieur- und Kfz-Sachversta¨
ndigenb€uro Priester und Weyde, Saarbr€ucken, Berlin, Subscripts
2004. a ¼ actual
[16] A. Pugsley and M. Macaulay, The large scale crumpling of car ¼ car
thin cylindrical columns. Qt. J. Mechanics Appl. Math. 13 ccs ¼ collision closing speed
(1) (1960), pp. 1
9.
eff ¼ effective
[17] B. Schmidt, CAARS, Reconstruction Specialists, Confer-
ence on Motorcycle Crash Investigation and Reconstruc- m/c ¼ motorcycle or scooter
tion, Santa Rosa, CA. 2004. oa ¼ overall
[18] J. Searle, The Reconstruction of Speed in Motorcycle Colli- p ¼ predicted
sions for the Extent of Damage, Road Accident Analysis, t ¼ total
Downloaded by [Istanbul Universitesi Kutuphane ve Dok] at 10:50 20 December 2014

Impact, ITAI, Shrewsbury, Spring, 2010.

w ¼ wheelbase
[19] D.M. Severy, M.D. Harrison, and D.M. Blaisdel, Motorcy-
cle collision experiments, SAE paper 700897, Society of
Automotive Engineers Inc., Warrendale, PA, 1970, pp. Abbreviations
67
120. SE ¼ specific energy (Nm/kg)
[20] M. Weyde and J. Priester, Motorcycle crash tests at a high
speed level against standing and moving passenger cars,
17th annual conference of the EVU, European Association
for Accident Research and Analysis, Nice, France, 6
8 Appendix 2.
November 2008, pp. 125
142. Table A2. Motorcycles and scooters used in barrier tests.
[21] D.P. Wood, A model for the frontal impact crashworthi-
ness of the car population, The Fourth International Con- Scooters Motorcycles
ference on Structural Failure, Product Liability and
Technical Insurance, Vienna, Austria, 1992. Piaggio Zip Kawasaki 1000
[22] D.P. Wood, Collision speed estimation using a single nor- Gilera Runner Honda CB400N
malised crush depth-impact speed characteristic, SAE
Kymo DJ50 Hercules K125
920604, Society of Automotive Engineers Inc.,
Warrendale, PA, 1992. Peugeot Buxy Yamaha XS400
[23] D.P. Wood, M. Doody, and S. Mooney, Application of a gen- Piaggio NRG Honda CM400
eralised frontal crash model of the car population to pole Asprillia SR50 Suzuki GSX250
and narrow object impacts, SAE paper 930894, Society of Asprillia Rally
Automotive Engineers Inc., Warrendale, PA, 1993.
Peugeot Speedflight 2
[24] D.P. Wood, C. Glynn, and D. Walsh, Estimation of the colli-
sion speed in a collision of a motorcycle or scooter with a
car from individual vehicle deformation, Proc IMechE Part
D: J. Automobile Eng. 228 (2014), pp. 295
309.
[25] D.P. Wood, C. Glynn, and D. Walsh, Motorcycle-to-car
and scooter-to-car collisions: speed estimation from per- Appendix 3. ‘Force
Balance’ model derivation
manent deformation, Proc IMechE Part D: J. Automobile
Eng. 223 (2009), pp. 737
756.  
1 Mm=c Mcar;eff
Et ¼ V2 ; A1
2 Mm=c þ Mcar;eff ccs

Appendix 1.
Et ¼ Em=c þ Ecar : A2
Notation
d ¼ deformation (m) But
E ¼ energy (Nm) Ecar ¼ Em=c
dcar
: A3
h ¼ offset of the line of action of the motorcycle/ dw
scooter velocity vector (m)
k ¼ radius of gyration (m) Therefore, combining Equations (A2) and (A3):
kph ¼ kilometres per hour
l ¼ length of car (m) Em=c ðdw þ dcar Þ
M ¼ mass (kg) Et ¼ : A4
dw
P ¼ two-tailed p-test value
r2 ¼ coefficient of determination
 552 D.P. Wood et al.

Equation (A3) is force match of motorcycle and car dynamic and

deformations. Analysis found that for motorcycles/scooters
dw;dynamic ¼ dw þ 0:1; and for cars that dcar;dynamic ¼ dcar þ 0:05
from [18] as, post collision, the permanent/residual deformations SE ¼ 641:7ðdw þ 0:1Þ1:89 ; A7
are measured. These values are substituted into Equation (A4) to
yield therefore,

Em=c ðdw þ dcar þ 0:15Þ Et ¼ Mm=c 641:7ðdw þ 0:1Þ0:89 ðdw þ dcar þ 0:15Þ: A8
Et ¼ : A5
dw þ 0:1
Combining Equations (A1) and (A8) yields
As   12
Mm=c 0:89
Vccs ¼ 1283:4 ðdw þ 0:1Þ ðdw þ dcar þ 0:15Þ :
Moa
Em=c ¼ SE  Mm=c A6
A9
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Table A4. 107 staged tests.

Speed Speed
Test of M/C of car
no. Reference Motorcycle type (kph) Car type (kph) Point of contact Angle

1 Kasanicky et al. [11] Babetta Moped 41 Opel Rekord 0

Nearside behind the front wheel 90
2 Kasanicky et al. [11] Suzuki GSX 400 86 VW Golf II 0
Nearside behind the front wheel 90
3 Kasanicky et al. [11] Yamaha XS 400 78 VW Polo Combi 0
Nearside centre 90
4 Kasanicky et al. [11] Yamaha XS 400 122 Mazda 323 0
Nearside front wheel area 90
5 Kasanicky et al. [11] Yamaha XS 360 117 Skoda Favorit 0
Nearside front door area 90
6 Kasanicky et al. [11] Honda CB 400N 98 Toyota Camry 0
Nearside front of the rear door 90
7 Priester and Weyde 05 [13] Honda CB 400N 81 Seat Ibiza 0
Offside behind the front wheel 135
8 Priester and Weyde 05 [13] Gilera Runner 49.1 Mazda 323 0
Centre of offside 45
9 Priester and Weyde 05 [13] Gilera Typhoon 47.9 Mazda 323 0
Centre of nearside 70
10 Kasanicky et al. [11] Suzuki RG 125 49.2 Mitsubishi Cordia 27
Behind offside front wheel 105
11 Kasanicky et al. [11] Kawasaki GPZ 750 60.4 Moskvic 412 17
Offside between the centre and front 60
wheel
12 Priester and Weyde 05 [13] Yamaha XS 400 81 Daihatsu 16 Offside front wheel area 135
13 Priester and Weyde 05 [13] Suzuki XJ 400 95.3 Audi 100 29.5 Offside behind the front wheel 135
14 Priester and Weyde 00 [14] Honda CB 400 N 98 Mitsubishi Colt 0 Right front door 15 cm in front of 90
B-pillar
15 Priester and Weyde 00 [14] Honda CB 250 N 100 Peugeot 305 0 Centre of right rear door 90
16 Priester and Weyde 00 [14] Suzuki GSX 400 100 Renault 21R 0 Right side, before right A-pillar 90
17 Priester and Weyde 00 [14] Honda CB 250 N 99 Honda Accord 0 Left side, B-pillar 90
18 Priester and Weyde 00 [14] Honda CB 250 N 100 VW Passat 0 Front right corner, 50 cm forward of 90
front axle
19 Priester and Weyde 00 [14] Yamaha XS 360 99 VW Scirocco 0 Right door, centre 90
20 Priester and Weyde 00 [14] Yamaha XS 360 99 Audi type 86 0 Right door, centre 90
21 Adamson et al. [1] Kawasaki 1000 (1990) 48 Car (maroon Thunderbird) 0 Right front wheel 90
22 Adamson et al. [1] Kawasaki 1000 (1990) 48 Car (maroon Thunderbird) 0 Front bumper 15 cm right of centreline 90
23 Adamson et al. [1] Kawasaki 1000 (1990) 68 Car (silver Thunderbird) 0 Right door centre 90
24 Adamson et al. [1] Kawasaki 1000 (1990) 79 Car (silver Thunderbird) 0 Body left rear, fender between wheel 90
well and bumper
25 Adamson et al. [1] Kawasaki 1000 (1990) 66 Car (silver Thunderbird) 0 Right front fender, between wheel well 90
and bumper
26 Adamson et al. [1] Kawasaki 1000 (1990) 63 Car (maroon Thunderbird) 0 Body left rear, between the wheel well 90
and bumper
27 Adamson et al. [1] Kawasaki 1000 (1990) 55 Car (maroon Thunderbird) 0 Rear bumper, 43 cm left of the right 90
end
28 Adamson et al. [1] Kawasaki 1000 (1990) 72 Car (silver Thunderbird) 0 Front bumper, right of centre 90
29 Adamson et al. [1] Kawasaki 1000 (1990) 74 Car (maroon Thunderbird) 0 Body, between B-pillar and left rear 90
wheel well
30 Severy et al. [19] Honda CB 350 32 Plymouth Sedan 0 Right front door 90

(continued)
 International Journal of Crashworthiness 553

Table A4. (Continued )

Speed Speed
Test of M/C of car
no. Reference Motorcycle type (kph) Car type (kph) Point of contact Angle

31 Severy et al. [19] Honda CL 90 48 Plymouth Sedan 0 Left front door 90

32 Severy et al. [19] Honda CB 350 48 Plymouth Sedan 0 Driver’s door 90
33 Severy et al. [19] Honda CB 350 48 Plymouth Sedan 0 Right front door 90
34 Severy et al. [19] Honda CB 350 48 Plymouth Sedan 0 Right front wheel 90
35 Severy et al. [19] Honda CB 750 48 Plymouth Sedan 0 Right front door 90
36 Severy et al. [19] Honda CB 350 64 Plymouth Sedan 0 Driver’s door 90
37 Priester and Weyde 04 [15] Kymco DJ 50 49 Opel Kadett 0 Right front wheel 90
38 Priester and Weyde 04 [15] Kymco DJ 50 61 Opel Kadett 0 Left front wheel 90
39 Priester and Weyde 04 [15] Peugeot Zenith 60 Opel Kadett 0 Left front wheel 90
40 Priester and Weyde 04 [15] Yamaha Aerox 42 Opel Kadett 0 Driver’s door 90
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41 Priester and Weyde 04 [15] Peugeot Buxy 63 Opel Kadett 0 Right front door 90
42 Priester and Weyde 04 [15] Piaggio NRG 30 Opel Kadett 0 Right front wheel 90
43 Priester and Weyde 04 [15] Gilera Runner 52 Opel Kadett 0 Left front wheel 90
44 Priester and Weyde 04 [15] Sukuki GT 1100 75 Opel Kadett 0 Left front door 90
45 CTS, test 10402 [5] Yamaha XZ 550 55.7 Ford Escort III 0 Left side, rear door 90
46 CTS, test 14613 [8] Kawasaki GPZ550 110.9 Nissan Sunny 0 Offside front door, near hinge 90
47 Craig [4] Yamaha Virago 108.63 Dodge B 100 Van 0 Nearside centre 90
48 CTS, test 16225 [9] Yamaha XJ550 88 VW Golf 10 Nearside rear door 90
49 CTS, test 16226 [10] Kawasaki GPZ550 87 Saab 9000 8 Nearside front door, near hinge 90
50 Prester and Weyde 08 [20] Kawasaki GPZ 400 80 VW Polo 15 Nearside rear door 90
51 CTS, test 11382 [7] Yamaha XS 750 72 VW Polo 0 Nearside front door centre 80
52 CTS, test 11374 [6] Yamaha XS 850 72 VW Polo 0 Nearside front door centre 100
53 Searle - CAARS [18] Not specified 48 Not specified 0 C-pillar/axle 90
54 Searle - CAARS [18] Not specified 64 Not specified 0 Driver’s door 90
55 Searle - CAARS [18] Not specified 50 Not specified 0 A-pillar 90
56 Searle - CAARS [18] Not specified 74 Not specified 0 Passenger door 90
57 Searle - CAARS [18] Not specified 83 Not specified 0 Passenger door 90
58 Searle - CAARS [18] Not specified 83 Not specified 0 Side of front fender 90
59 Searle - CAARS [18] Not specified 60 Not specified 0 C-pillar 90
60 Searle - CAARS [22] Not specified 74 Not specified 0 A-pillar 90
61 Searle - CAARS [18] Not specified 84 Not specified 0 Side of front fender 90
62 Searle - CAARS [18] Not specified 72 Not specified 0 Passenger door 90
63 Searle - CAARS [18] Not specified 64 Not specified 0 Rear panel 90
64 Searle - CAARS [18] Not specified 72 Not specified 0 Rear door 90
65 Searle - CAARS [18] Not specified 56 Not specified 0 Side of front door 90
66 Searle - CAARS [18] Not specified 51 Not specified 0 Driver’s door 90
67 Searle - CAARS [18] Not specified 61 Not specified 0 B-pillar 90
68 Searle - CAARS [18] Not specified 64 Not specified 0 A-pillar 90
69 Searle - CAARS [18] Not specified 106 Not specified 0 Rear door 90
70 Searle - CAARS [18] Not specified 50 Not specified 0 Rear panel 90
71 Searle - CAARS [18] Not specified 60 Not specified 0 A-pillar 90
72 Searle - CAARS [18] Not specified 80 Not specified 0 Frontal 90
73 Searle - Grandel [18] Not specified 60 Not specified 0 Front door 90
74 Searle - Priester 02 [18] Not specified 100 Not specified 0 Front door 90
75 Searle - Priester 02 [18] Not specified 95 Not specified 0 Front door 90
76 Searle - Priester 02 [18] Not specified 96 Not specified 0 A-pillar/wheel well 90
77 Searle - Priester 02 [18] Not specified 96 Not specified 0 Front wheel/overhang 90
78 Searle - Priester 02 [18] Not specified 99 Not specified 0 Front door 90
79 Searle - Priester 02 [18] Not specified 97 Not specified 0 Front door/A-pillar 90
80 Searle - Zilina [18] Gilera RX 125 39 Opel Rekord 0 Rear impact 90
81 Bartlett 13 - CAARS 09 [2] 1979 Suzuki GS 550E 73.2 1986 Honda Accord 0 208 cm behind front axle 90
82 Bartlett 13 - CAARS 09 [2] 1983 Yamaha XJ750M 64.5 1986 Honda Accord 0 43 cm forward of front axle, big 90
rotation
83 Bartlett 13 - CAARS 09 [2] 1983 Honda VT 750C 57.8 1986 Honda Accord 0 137.16 forward of rear axle (near CG) 90

(continued)
 554 D.P. Wood et al.

Table A4. (Continued )

Speed Speed
Test of M/C of car
no. Reference Motorcycle type (kph) Car type (kph) Point of contact Angle

84 Bartlett 13 - CAARS 09 [2] 1981 Kawasaki KZ440D 61.0 1986 Honda Accord 0 Just ahead of RR axle 90
85 Bartlett 13 - CAARS 09 [2] ‘83 Honda CB550 73.2 1989 VW Golf 0 Just rear of F axle 90
Nighthawk
86 Bartlett 13 - CAARS 09 [2] 1982 Honda CM450C 75.6 1989 VW Golf 0 B-pillar 90
87 Bartlett 13 - CAARS 09 [2] 1981 Kawasaki KZ440D 66.5 1989 VW Golf 0 LR axle 90
88 Bartlett 13 - CAARS 09 [2] 1980 Kawasaki KZ440 B 86.9 1989 Nissan Maxima 0 43 cm rearward of LR axle 90
89 Bartlett 13 - CAARS 09 [2] 1986 Suzuki LS650 Savage 88.5 1989 Nissan Maxima 0 86 cm rearward of RF axle 90
90 Bartlett 13 - CAARS 09 [2] 2004 Kawasaki EX250]F 87.9 1989 Nissan Maxima 0 RR axle 90
91 Bartlett 13 - CAARS 09 [2] ‘88 Honda CBR600F Hurr. 90.0 1989 Nissan Maxima 0 96.5 cm forward of RR axle 90
92 Bartlett 13 - CAARS 09 [2] 1979 Suzuki GS550 90.6 1989 Honda Civic 0 58 cm forward of RR axle 90
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93 Bartlett 13 - CAARS 09 [2] 1981 Yamaha Seca 750 92.2 1989 Honda Civic 0 left A-pillar, 58 cm rearward of LF 90
axle
94 Bartlett 13 - CAARS 09 [2] 1982 YarL XV920 Virago 90.8 1989 Honda Civic 0 LR axle 90
95 Bartlett 13 - CAARS 09 [2] 1990 Kawasaki EX500A 98.0 1992 Mercury Tracer 0 91 cm rear of RF axle 90
96 Bartlett 13 - CAARS 09 [2] 1982 Si.id GS750 96.2 1992 Mercury Tracer 0 LR axle 90
97 Bartlett 13 - CAARS 09 [2] 1980 Sim.id GS750 95.4 1992 Mercury Tracer 0 48 cm rear of RR axle 90
98 Bartlett 13 - CAARS 09 [2] ‘86 Suzuki VS700GL 71.3 1986 Mercedes 300E 0 RF axle 90
Intruder
99 Bartlett 13 - CAARS 09 [2] ‘85 Honda CB650 77.9 1986 Mercedes 300E 0 99 cm rear of LF axle 90
Nighthawk
100 Bartlett 13 - CAARS 09 [2] 1987 Suzuki GSXR750 76.8 1986 Mercedes 300E 0 30 cm rear of RR axle 90
101 Bartlett 13 - CAARS 09 [2] 1983 Suzuki GS1100ES 79.0 1986 Mercedes 300E 0 71 cm rear of LR axle 90
102 Bartlett 13 - CAARS 09 [2] 1978 Honda CB750 H-matic 48.0 1988 Honda Prelude 0 119 cm rear of LF axle 90
103 Bartlett 13 - CAARS 09 [2] ‘90 Honda Pac. Cst. PC800 52.9 1988 Honda Prelude 0 RR axle 90
104 Bartlett 13 - CAARS 09 [2] 1984 Honda Goldwing 1200 94.6 1988 Honda Prelude 0 89 cm rear of front axle, near F pillar 90
105 Bartlett 13 - CAARS 09 [2] 1978 Suzuki GS1000 97.0 1988 Honda Prelude 0 RR 90
106 Craig 12 [3] 1993 Kawasaki ZX600-C 44.1 2006 Chev. Impala 0 Passenger door 90
107 Craig 12 [3] 1978 Honda CX-500 48 2006 Chev. Impala 0 Left rear door 90

Appendix 4.

Figure A4. Collision angle range.