TINCE2016 - Impact load curve for commercial aircrafts: a normalized model – P.M. Alliard, J....
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Transcript of TINCE2016 - Impact load curve for commercial aircrafts: a normalized model – P.M. Alliard, J....
3rd Conference on Technological Innovations in Nuclear Civil Engineering
Full paper Submission, TINCE-2016 Paris (France), September 5th – 9th, 2016
Impact load curve for commercial aircrafts: a normalized model
Pierre-Marie Alliard1, Jacques Chataigner2
1Project director, Tractebel Engie, Coyne et Bellier, Nuclear and Industry, Lyon Agency, TourPart-Dieu - 129, rue Servient, 69326 Lyon CEDEX 3 – France([email protected])2Techical director, Tractebel Engie, Coyne et Bellier, Nuclear and Industry, Lyon Agency, TourPart-Dieu - 129, rue Servient, 69326 Lyon CEDEX 3 – France([email protected])
Introduction
Safety requirements of nuclear new built projects have considered airplane crash (APC)
hazards for many years, but mostly those regarding general and military aviation. Since 09/11
events, the need to assess the risk of commercial APC has been highlighted. As a result, guide-
lines were developed to support regulators, designers and owners of nuclear facilities with re-
spect to the commercial APC analysis (see [SIE15]). Furthermore, regulators’ position is evolv-
ing, as new requirements make this load case no longer limited to malevolent acts, but also con-
sider it as possible accidental situations.
Many papers already presented APC load time functions F(t), obtained either by means of
simplified decoupled methods or integral missile target dynamic interaction methods. First work
on that topic that initiated in 1968 (see [RIE68]), for the B707-320 and B720 aircrafts, resulted in
the Riera method. Then, complementary sets of load curves were issued such as those for
A320, B767 and B747 (see [ARR07], [BYE11], [HEN07], [IAE14], [ILI11], [JIN11], [KOS11],
[KYO13], [OEC02], [RIE80], [SEA11], [VUO11], [XIN15]). All these methods for APC analysis
have common drawback that they need to collect detailed input data about one given aircraft for
each project, either mass distribution and crush force, or high quality finite element models of the
aircraft when carrying out the integral approach. On the contrary, some regulators define APC
load case only by means of two governing parameters (aircraft total mass and speed at impact),
although no simple formula currently exists in design codes to correlate these data to F(t). There
is a lack of a practical and normalized model for engineering applications.
3rd Conference on Technological Innovations in Nuclear Civil EngineeringTINCE 2016, Paris 5th to 9th September
This paper proposes a general normalized formula to define APC load F(t) only depending
of the airplane mass and speed. Besides, a reduction factor is provided to assess the effect of
spent kerosene between take-off and the crash.
This work was based on the analysis of public technical data (available characteristics of
commercial aircraft and already published load curves). No confidential information relative to
any specific project is revealed.
General assumptions
For an impact normal to a rigid wall, Riera’s method ([RIE69] and [RIE80]) is based onfundamentals equations (1) and (2):
[ ( )] = [ ( )] (1)
( ) = ( ) [ ( )] (2)
where F(t) is the APC load time function (LTF) ; Mimpact is the aircraft mass when crash occurs at
time t=0 ; Fc is the buckling force of the aircraft structure ; µ(x) is the mass distribution of the
aircraft per unit length ; m is the crushed mass, x is the distance from nose of aircraft (crushed
length at the instant t).
In the present paper, two additional assumptions are introduced to develop a simplified
method.
Assumption (1): practice of Riera’s method has shown that in most of cases, when the ini-
tial velocity is sufficiently high, the buckling force is not significant compared to inertial forces
(see [IAE14]). For example, [ILI11] shown that even large errors (10%) in assessment of crush-
ing force have little effect on the load curve. So, let’s first consider that Fc 0. Validity domain of
this approximation is illustrated further in this paper. As there is no assumed rigidity, the entire
length of the aircraft is crushed during the impact. Velocity remains constant (equation (1) is re-
placed by equation (3)) and the crash duration is given in equation (4):
= (3)
= (4)
Where V is the aircraft speed when crash occurs; L is the length of the aircraft ; and tcrash is the
duration of the impact to crush the complete length of the aircraft. Then, equation (2) becomes
after integration:
3rd Conference on Technological Innovations in Nuclear Civil EngineeringTINCE 2016, Paris 5th to 9th September
( ) = (5)
( ) =²
(6)
Assumption (2): it is considered in the normalized method that all commercial aircrafts
share similar geometrical features, and equivalent mass distribution.
Normalized aircraft
A detailed inventory of aircraft characteristics was made based on manufacturers technical
data (see [AIR16] and [BOE16]). It was noticed that simple relationships exists between the air-
craft maximal take-off weight M0 and its dimensions (Figure 1). This led to propose the following
formulae to define the normalized aircraft as a function of the mass:
= 16,7 ln( ) 30,2 (7)
= 0,0082 + 3,5 (8)
2 = 6 , (9)
Where M0 is expressed in tons; and L, and b are in meter.
Figure 1 illustrates how these formulae were defined (dark trend curves). It shows that assump-
tion 2, according to which dimensions should be proportional to / (yellow curves), is almost
respected.
A normalized surface of impact is also provided in Figure 1.
Normalized load time function
Assumption (2) enables to carry out APC analysis by the means of two dimensionless
numbers t[norm] and F[norm]:
[ ] = =/
(10)
[ ] = =²/
(11)
3rd Conference on Technological Innovations in Nuclear Civil EngineeringTINCE 2016, Paris 5th to 9th September
Figure 1. Inventory of various commercial aircrafts characteristics (maximal take-off weight M0,fuselage diameter , length L, wingspan 2b) and normalized surface of impact
Figure 2. Normalized APC load time function (full tanks and partially filled tanks)
(M0)
b(M0)
2b
b/15
3rd Conference on Technological Innovations in Nuclear Civil EngineeringTINCE 2016, Paris 5th to 9th September
As recalled by [SIE15], all F(t) functions have in common expected curve characteristics:
first an increase after the impact of the cockpit appears ; then the load level stays constant till
the impact of the engines and the wingbox which causes a large increase ; finally the load level
decreases to zero in the last part. So, based on the observation of a large range of available
APC studies {M0, V} in recent papers, a normalized curve is provided on Figure 2 to estimate the
reaction at the interface between the collapsed aircraft at maximal mass M0, and a rigid wall.
It can be easily checked that the area below the curve F(t) equals the impulse M0V as as-
sumed by equation (5).
APC analyses usually consider the maximal take-off weight M0 of the aircrafts, whereas a
significant part Mspent should be subtracted due to the consumption of kerosene during taxiing at
the airport, take-off and flight. The remaining aircraft mass Mimpact at the instant of the crash is
actually:
(12)
As fuel tanks are located in the wings, it is considered that kerosene consumption only al-
leviates the peak value Fmax of the APC load time function. For an aircraft with partially filled
tanks, the corrected maximal force Fmax,reduced is deduced in equation (13) from the diminution of
impulse momentum MspentV, as represented on Figure 3:
= ) 0,33 (13)
Figure 3. Diminution of the maximal force due to consumption of kerosene
Finally, the normalized APC formula, depending on the amount of kerosene consumed
since take-off, is defined in Figure 2 at the previous page.
3rd Conference on Technological Innovations in Nuclear Civil EngineeringTINCE 2016, Paris 5th to 9th September
To enable efficient practice of the normalized method, some charts are provided in next
Figures 4. Two “envelope” situations are compared:
- APC a few minutes after take-off (full kerosene tanks gauge)
- APC after hours of flight (low kerosene tanks gauge) when the spent mass equals 30%
of the initial take-off weight.
It may be noticed that, in this normalized model, the load time function is highly dependent
on the onboard fuel mass: the maximal value Fmax is divided by two when APC occurs at the end
of commercial flight, in comparison with a crash at maximal weight.
Figure 4. Charts of the normalized APC formula for various cases {M0, V}
3rd Conference on Technological Innovations in Nuclear Civil EngineeringTINCE 2016, Paris 5th to 9th September
Recommended domain of validity
According to assumption (1), the bucking force of the aircraft is not significant compared to
the mass flow terms ( [ ] ), so that the velocity is constant during the impact, and the
complete length of the aircraft is crushed. It is proposed that this assumption is acceptable within
5% error, when the following criterion is checked:
1,5 <. ²
(14)
Where Fcf is the buckling force of the fuselage; 1,5 Fcf is the average buckling force along the
aircraft frame structure ; and MimpactV²/L is the average inertial force.
The mean value of the axial crushing force of a dynamically loaded thin walled cylinder can
be approximated as (see [VUO11]):
= (29,4 + 11,9) (15)
Where 0 is the yield strength, H is the tube shell thickness, and the diameter.
According to [RUC10] and [XIN15], usual structures are built with a grade 0 500 MPa alumini-
um and steel alloy. Finally, the corresponding estimation of the buckling force is illustrated on
Figure 4, as a function of the aircraft mass (since it is itself related to the dimensions; due to the
similitudes conditions of assumption (2)).
The criterion of equation (15) is plotted on Figure 5. It is shown that, the recommended
domain of use of the normalized method proposed in this paper may be:
M0 > 100 tons (medium and large commercial aircrafts)
v > 150 m/s when the crash occurs at maximal weight
v > 160 m/s when fuel tanks are almost empty
In the scientific and industrial community, expert opinions widely differ as regard the air-
craft velocity when impact occurs; as a matter of fact, depending of the project or the designers,
this parameter may range from 100 m/s ( landing velocity) up to 180 m/s. Moreover, regulators
requirements are usually between 150 m/s and 200 m/s for large commercial aircrafts, so that
the normalized method remains appropriate.
3rd Conference on Technological Innovations in Nuclear Civil EngineeringTINCE 2016, Paris 5th to 9th September
Otherwise, when used outside the domain of validity,
the force Fmin may be underestimated at the beginning of the impact when the fuse-
lage is being crushed
on the contrary, the peak value Fmax and the force at the end of the impact may be
overestimated because the aircraft speed decreases due to the buckling strength.
the crash duration assessment may not be accurate due to speed reduction
Figure 6. Recommended validity domain {M0, V} of the normalized formula
Comparison between proposed LTF normalized model and existing LTF curves
To validate the model proposed in this paper, the LTF normalized curve will be further oncompared to available LTF curves. It must be reminded that the latter were obtained from vari-
ous authors, by different methods (decoupled Riera’s method, or integral FE approach), for alarge range of aircrafts and different impact velocities.
Regarding APC at maximal weight with full kerosene tanks (see Figure 6), main commentsabout results from this comparison are:
for small aircrafts: all studied conditions {M0, V} do not fit with the recommended
validity domain of the normalized method. For the B707 at 103 m/s, red curve
shows that the back of the aircraft should be actually not crushed due to low kinetic
energy. For the A320 at 120 m/s, green curve seems to confirm that the buckling
force has significant effects at low velocity.
for medium size aircrafts: normalized method seems to be satisfactorily suitable
and good correlation between the different curves is noted, but the normalized
method slightly underestimates the crash duration.
3rd Conference on Technological Innovations in Nuclear Civil EngineeringTINCE 2016, Paris 5th to 9th September
for large aircrafts: the normalized formula provides results similar to those obtained
from available LTF curves, even at low speed. It is also remarkable that for the
B747, every author considered a different mass distribution, so that the resulting
LTF curves have different shapes.
Figure 6. Comparison of available load time functions with the normalized method (full tanks)
3rd Conference on Technological Innovations in Nuclear Civil EngineeringTINCE 2016, Paris 5th to 9th September
Figure 7. Comparison of available load time functions with the normalized method
Concerning APC with partially filled tanks (see Figure 7), conclusions are:
for medium and large aircrafts, the normalized method offers results which are
consistent with other estimations. However, level of similitude is smaller than for
APC at maximal weight, due to the very simplified approach. Besides, conditions
{M0, V} are outside the recommended domain of use of the normalized method.
there is a lack of available functions F(t) (only two aircrafts have been studied)
Example of application
Let’s consider an accidental APC safety requirement defined by Mimpact = 400 tons and V =
200 m/s. Load case #1 is a B747 aircraft, crashing several minutes after take-off (M0 = 413
tons ; Mspent = 13 tons). Load case #2 is an A380 aircraft, crashing after hours of flights (M0 = 560
tons ; Mspent = 160 tons). The normalized method enables to asses easily the two load time func-tions (Figure 8).
Then, the dynamic amplification can be computed: it is observed that, for a same impact-
ing mass, the most penalizing case is a relatively smaller aircraft with a high volume of fuel
onboard, instead of a larger aircraft close to dry weight.
3rd Conference on Technological Innovations in Nuclear Civil EngineeringTINCE 2016, Paris 5th to 9th September
Figure 8. Application of the normalized method for two 400 tons aircrafts
Conclusions
The methods presented in this paper to determine LTF curves was proved to be interesting
for validation of advanced finite element calculations of structures submitted to APC load cases,
at basic design stage of a specific project. Moreover, as it is normalized and practical, it could be
envisaged to introduce it in future revisions of APC shells design codes. Then, to anticipate a
possible increase of the aircrafts dimensions in the next century, the method also enables to
generate theoretical LTF curves representing larger aircrafts than A380.
Compared to LTF curves available for public documentation, for different conditions (mass,
velocity), it is remarkable that the normalized formula is slightly envelop in most cases, this being
due to the assumption that the total kinetic energy is transformed into the impact force against
the target wall, without any energy losses (neglected thermal effects and buckling force of the
aircraft frame structure). Therefore, it is sometimes admitted to introduce an additional corrective
factor = 0,9 to the aircraft mass to simulate such losses (see [KYO13], [NEI11]).
Eventually, in order to reach final validation of the normalized formula, it would be neces-
sary to enrich the available LTF database with some other aircrafts. In particular, further investi-
gations should be done regarding other aircrafts such as the A380, for which the size and
strength of fuselage is uncommon, and the B787 Dreamliner whose frame structure is made with
carbon composite materials. Besides, accurate modeling of fuel effects is still a challenge, even
if some enhancements are being done such as the Smooth Particle Method (see [HEN15]).
3rd Conference on Technological Innovations in Nuclear Civil EngineeringTINCE 2016, Paris 5th to 9th September
References
[AIR16] Airbus technical data (http://www.airbus.com/support/maintenance-engineering/technical-data)[BOE16] Boeing and McDonnel Douglas technical data
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Nuclear Engineering and Design, 237(12), pp. 1241-1249[HEN07] Henkel, F.O., and Dietrich, K. (2007). “Variants of analysis of the load case airplane
crash”, Transactions, SMiRT-19, Toronto, Canada – August, 2007, Paper ID J03/2.[IAE14] IAEA (2014). “Safety Aspects of Nuclear Power Plants against Human Induced External
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[KOS11] Kostov, M., Henkel F.O. and Andonov A. (2011). “Safety assessment of A92 reactorbuilding for large commercial aircraft crash”, Transactions, SMiRT-21, New Delhi, India –November 6-11, 2011, Div-VII: Paper ID#222.
[KYO13] Kyoungsoo, L., Sang Eul, H., Jung-Wuk, H. (2013). “Analysis of impact of large com-mercial aircraft on a prestressed containment building”, Nuclear Engineering and Design,265, pp. 431-449.
[NEI11] NEI 07-13, “Methodology for Performing Aircraft Impact Assessments for New PlantDesigns”, Nuclear Energy Institute, Revision 8P, April 2011
[OEC02] OECD/NEA (2002), Specialist Meeting on External Hazards.[RIE68] Riera, JD. (1968). “On the stress analysis of structures subjected to aircraft impact forc-
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aircraft impact”, Nuclear Engineering and Design, 57, pp. 193-206.[RUC10] Ruch, D. and Muller, H.S (2010). “Determination of Load-Time Functions due to Impact
of Soft Missiles”, 8th fib PhD Symposium, Kgs. Lyngby, Denmark June 20 – 23, 2010.[SIE11] Siefert, A., and Henkel F.O. (2011). “Non-linear analysis of commercial aircraft impact
on a reactor building – comparison between integral and decoupled crash simulation”,Transactions, SMiRT-21, New Delhi, India – November 6-11, 2011, Div-III: Paper ID 144.
[SIE15] Siefert, A., and Henkel F.O. (2015). “The load case aircraft impact: state of the art andgeneral investigation procedure”, Transactions, Post-SMiRT-23, Istanbul, Turkey – Octo-ber 21-23, 2015.
[VUO11] Vuorinen, M., Varpasuo, P. and Kähkönen, J. (2011). “Reaction time response of alarge commercial aircraft”, Proc., 19th International Conference on Nuclear Engineering,ICONE19-43207, Chiba, Japan, May 16-19, 2011
[XIN15] Xinzheng, L., Kaiqi L., Song C., Zhen X. and Li L. (2015). “Comparing different fidelitymodels for the impact analysis of large commercial aircrafts on a containment building”,Engineering failure analysis, 57, pp. 254-269.
3rd Conference on Technological Innovations in Nuclear Civil EngineeringTINCE 2016, Paris 5th to 9th September
Please fill in the blanks at the end of this extended abstract (the additional blue lines andpotential page it may generate are not accounted in the number of pages)
Preference: Poster Oral
Topic: 1 - Advanced Materials 2 - Design and Hazard Assessment 3 - Civil Works Construction 4 - Long Term Operation & Maintenance 5 - Dismantling of civil works & Civil Works in Hostile Environment 6 – Geotechnical Design & Construction & Fluid Structure Interaction
Corresponding author: [email protected]
.