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.

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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:


( ) = (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)


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


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.


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}


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.


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.


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)


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.


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]).


References

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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

Events: Assessment of Structures”, Draft Safety Report DD1087, 16 December 2014.[ILI11] Iliev, V., Georgiev, K. and Serbezov, V. (2011). “Assessment ofimpact load curve of boe-

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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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[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

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http://www.airbus.com/support/maintenance-engineering/technical-data

http://www.boeing.com/commercial/airports/plan_manuals.page


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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]

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