A description of a special type of seismograph, called a "landing-shock recorder," to be used for measuring the acceleration during impacts such as are experienced in airplane landings, is given . The theory, together with the assumptions made, is discussed in its relation to calculating the acceleration experienced in impact. Calculations are given from records obtained for two impacts of known acceleration. In one case the impact was very severe and in the other it was only moderately severe

Brevoort, M J

English

NASA Technical Reports Server

r FILE C';'""' , r '0. 
T:<1CHlH CAL liOTES 
NATIONAL ADV I SORY COl.:IHT'I'3E FOR ~\'ERO:1AUTICS 
No . 501 
LANDING - SHOCK RECORDER 
By M. J . Br ovoort 
Langley Eemorial Aeronautical Laboratory 
Washin Gton 
July 1 934 
FIl 
Y 
https://ntrs.nasa.gov/search.jsp?R=19930081251 2020-03-17T03:57:19+00:00Z

NATIonAL AnVI SORY COMMITTEE FOR AER011AUTI cs 
TECHNICAL NOTE NO . 501 
LANDING-SHOCK RECORDER 
By M. J. Br evo ort 
SUHMARY 
A descript ion of a special type of seismograph, 
called a "l an ding-shock recorder," to be used for measur-
ing the accelerat ion during impacts s~ch as are experienced 
in airplane lan dings, is g iven. The theory, together with 
t he assumptions made, is discussed in its relation to cal-
culating the acceler ati on experienced in impact. Calcu-
lations are giv en from records obtained for two impe,cts 
of known acceleration. In one case the imp act was very 
severe and in the other it was only moderatelY severe. 
INTRODUCTION 
At the time t h e development of the land ing-shock re-
corder was startod it was believed that the change in 
ma gni tude o f acceleration Qxpe ri enced in tho landing of 
an airplano was too rap id to be accuratoly rocorded by an 
ordinar y acceleromete r having a f ro quen cy of 6 0 vibra-
tions por socond. Also, as the accelerometer responds to 
struc tural vibrations , it often gives records which are 
almost unreadable . It wc),s believed that a.n instrument 
giving a t ime-disp lacement record during the impact due 
to landing woul d g i v e valuable infor ma tion not only about 
the char a cter of the land ing , but also about the reliabil-
it y of the accelerometers in use. Accordi ngl y , the 
National Advisor y Co mmittee for Aer onautics developed the 
design of the present landing-shock recorder, which is an 
i nstrument that furnishes a time-disp lacement histnry of 
movem en t in a given direction. 
DESCRIPTION OF THE INSTRUMENT 
A diagrammatic s k etch of the landing-shock recorder 
is given in figur e 1. Th e essential parts are a weight, 
2 N.A .C.A. Technical Note No. 501 
a supporting spring, and a recordin g mechani sm. The 
weight is restricted to move~e n t in a given direction by 
an e n closi ng cylinder and :i. s r:l D.de relatively frictionless 
by six ball bearings which ali n e it in the c ylinder . The 
spring, which supplies t'le necessary restoring force to 
the weight, is so chosen that the combination has a nat-
ural freqllency of about 1.5 vibrations per second. The 
connection between spr:lng and weight is so arranged that 
the movement of the weigJ.1.t relative to the base causes a 
mirror to rotate; the mirror thoreby rofl e cts a beam of 
li ght onto a moving film to give a time histo ry of the 
movement of the weight. Figur e 2 shows the original in-
strument as it was arranged for experimental purposes. 
The base, fi l m drum, and motor drive are those of a stand-
ard N.A.C.A. recording instrument. 
THEORY 
The e quation describing the relati on between the re-
sponse of a loaded s p r i ng and an imposed acceleration 
varying as ~2X~ is 
dt 2 
d 2_X + Dr d "-til (..2. \ + Ex 
d t 2 d t ) 
whore M is the active mass on tho spring 
D is the damping coefficient 
K is the con s t a.n t of the spring 
x is tho d i splaeemont of tho woight from the 
n outral p08ition 
Xl is t he di splaeement (from some fixed poin·t) of 
t he instrument base in a direction par allel 
to the axi B of the cyl i nder 
t is the time 
The instrumen t has been made relatively frictionloss, 
so the damping Df (9.!.) can be ne g lected. 
\ d.t .I 
B.A.C.A. Technical Notci No . 501 3 
Equation (1) can thus be rewritten 
(2) 
The two terms on the left of equation (2) account 
K for the imp 0 sed ac eel era t ion; t 11 e t e r m iA x g i v est he 
accelerat ion accounted for by the restori ng force of the 
sp ring , and is the acc~leration gi ven by the conventional -
d2 x type accelerome ter where is assumed to be zero. How-
dt 2 
ever, when spring-weight systems of very low frequency are 
s u bjected to accelerations of s h ort duration , the part 
d2 x 
d t 2 
may be predominant. The l a nding-shock recorder was 
designed to work under this latter co nd ition. Her e the 
term ~ accounts f or the predo~inant part of the acco1-
dt 2 
eration during i mVBct and, due to the low value fer K - . , 
ill . 
t h e term K x is usually more in t h e ordor of a correc-
1,1 
- tion. It is of interest to note the fact that co nven-
t i onal accelerometers alway s g ive readings in error by 
. t ll e amount of However, x is made very small in 
the conventional instrument, thus justifying its neglect 
in all cases except those in which t becomes so small 
t~lat the term becomes app reciable. It is conc eiv-
able that in sharp impact this latter possibility may be 
realized . It is a lso of inter e st to note that the true 
accelerat ion can be found in any case by taking into ac-
cO'Lmt both terms on the left side of equ ation (2). 
RESULTS 
.... 
In ordor to ch eck the performance o f the instrument 
and determine the accuracy of co mpu ting the acceleratioti, 
4 ' rl .A.C , A. Technical Note Ro. 501 
tho instrument was sub " octod to known accolo'rati ons simu"!' · 
lating impact conditi ons as no arly as p ossible. 
These known acceleratton s were i nd"l'.ced by a beam 
supported at each end , deflected at -t h o mi dp oint between 
t h e suppo r t s , and r el e as ed b~r a tr i gger. Wi t h the land-
i ng~~hock record e r located a t the midpoint of the beam, 
t~ e tri gger was released so as to g ive a series of im-
p l lsGS to t h o instrument. The deflection of tho be~m a t 
t ~le s t art of tho ini t i al imp u l so boin g known and si rr,:? ll3 
~ 4 armonic vibration be i n g assumed, the correspond i ng ac-
' ~eleration , a, is g iven by the reia~ion 
a = 4 TT 2 f 2 d ·c 0 s 2 TT f t 
wh ere f is the frequency of ,vibratio n. ' o f the beam and d 
is the d.eflection of the beam fro m t he rest po s::'t io!l . At 
zero time cos 2n ft = 1 , giv~n g an . i ni ti a l acceleration 
of a= 4n 2 f 2 d . The assumption o f s imp l e harmonic vi-
bration is reasonable, as the . deflec t i 0n WR S limi ted to 
less than 3 inches with a beam 1 0 f ee t 1 0 g an e. the beam 
su pports allowed no ve_tical movement at the end . 
As an illu stratio n o f . the . resu lts obtained with the 
landin g-shoc~ recor d er, a record is reproduced as figure 
3. The film sp eed for t h is reco d . was about 1 .25 inches 
per second . Time on the record i s given at I - second in-
tervals by the w l ite dots along the bottom of the film . 
A sample sheet of calcul a tio n s is g iven in table I . Fig-
ure 4 gives t h e cu rves for displacement , first difference 
~r ' The values determining the curv~ of ~~ against time 
could not be found with sufficient a ccuracy to justify 
d.r awi n g a curve mor e der i ni to than a stra.i ght 1 in e . as 
drawing a strai ght line involvos averaging over tho part 
of the cycle durin~ wh ich t h e acceleration varies least . 
Th e seco n d di f fe r ence is co n stan t , h aving a value of 3,400 
i l ./sec~ This valu e correspo nds to B . B g for 
~:!.. ad. din g , a v a1<.1. e 0 fl . 0 5 for K x ( see fig . 7) . the 
d t 2 ' Ivl ' 
total acceleration is 9. 8 g . Th is value co mpares with 
t h e value 9.5 6 g , calculated f rom t h e d isplacement of the 
beam. Th e beam had a ~r 8ql eu cy of 5 . 64 vi brations per 
s e co I- d and was g i v en a de f lec t ion of 2 . 65 inchos. Th ese 
v a ll' es give an acceler a tion of 8 • .) , , w:i.l ich , with 1 . 0 g 
Q,v. e to t h e acceler a ti on of gr avity. g ives. a tota.l acceler-
ation of 9 , '6 g , Th is is onl y one of several records that 
N.A.C.A. Technical ~oto No . 501 5 
were computed. All the r e cords gnv e results within 10 
percent of ·the co mpu ted acce l erat5.on, Wh ich is abo u.t the 
degree of accuracy to b e expe ct e d . RefineT!lon t s contem-
plated in tho in strumont for g on or a l us c will p robabl y 
reduco thi s error to about ±5 pe r cent . 
Figure 5 gives th e reco.rd of an air "O lane landing , 
5(a) being t he record from t h e landinG- shock recorder 
and 5 (b) the record f ro m an accelero meter. The acceler-
ometer h ad a f requenc y of 60 v ibrations per s e c ond and 
was abou t critically clamped . Th e complete results from 
the lan din ; -shock recorder f or the same l anding are given 
in table II and figure 6 . I n figure 6 are g iven the dis-
placement cu rvo for the weight on the sprin g , its veloc-
'J. dx 
l"vy "d1"' 
tion 0.2 x 
clt2 
its accel erati on d
2 X 
--, 
d t 2 
a !l d i ts tot al a c c e 1 e r a-
+ ! x. 
~.1 
Al l quantities except the total accel-
eration, which is gi ve n in multiples of g, are given in 
inches and seconds. The result s fr o m rec ord 5 (a) give an 
acceler a t i o n of 3.05 is at time 1.815 s econds , and the 
readings fr om record 5 (b) gi ve a n acceloration of 3.14 g 
at ti me 1. 85 secon ds . 
Tes ts of the land ing-sh ock recorder hav e indicated 
its v alue for determini ng the perfo r mance o f accelerome-
ters T!.l1Cler doubtfu l c andi tians a ne. for making me a. surement s 
to determine the a.cceler a tion s u nc1.er imp a.ct conditions. 
It can a lso b e used to adv antage on landin ~ tests where 
excessive vib r ation occur s , owing to its lack o f resonance 
to airplan e vibrations . 
A fu rt h er valuable resu lt of t h is development has 
been the increase in co n fidence in t h o st an dard N. A.C.A . 
recording accelerometer. Airp l a~e landing s h ave b een 
s h own to be of loss S!larp impact t l an was f ormor l y be-
lieved and co mp arison o f r0c or ds has shown tha.t tho ac-
celerometer h a s a suffici ently rapio. r c.sponso to record 
the maximum accel er at io n reli a bl y , ev en wi th a s mall a-
amount of overdamp ing . 
It is worth ment ion ing that, a l though evaluation of 
the records entails co nsid erable co mputati on and graphic-
6 B.A.C.A. Technical Note ro o 501 
al differen tiation, the proper re gi on of the record for 
anal ys is is readily recognized Bfter a lit tle experience, 
a nd the calculations c a n be quite e a sily mad e. 
Langley Menorial Aeron aut ical Laborato r y , 
National Advis:Jry Committee f or Aeronautics', 
Langley Field, Va., February 13, 1 934 . 
TABLE I 
Def l ect ion d2 x Time Deflection I dx 
s ec. fr om the of t he dt clt2 
r ecord weight in . / s ec . I in./sec. 
in. i~. 
0 .0025 0.000 0 .000 I 11.0 3400 I 
. 009 I .054 
I 16 . 0 3400 . U05 I I 
I . 0075 I 21. 0 3400 
I 
---
- --
, 
.010 . 024 . 144 I 31. 0 3400 I I 
. 0125 •043 . 253 45 . 0 ,,400 I .' 
.0150 . 064 
.334 --- 3400 
. 0175 . 091 ·540 I 
--- 31.~00 
. 01375 --- --- I ;J8 . 0 3400 
.0200 . 119 .714 I --- 31.tOG 
.02125 --- --- ~l.O 3400 
I 
d2 x 2 d x 
.8 dt
2 dt Z 
g 
I 8 .8 
g .8 
8 .S 
8 .8 
8 .8 
3 . 8 
I 8 .8 
8 . 13 
S .8 
8 .8 I 
+ Kx 
M 
g 
9 ·8 
9 ·8 
9 ·8 
9 ·8 
9 ·8 
9 ·0 
9 ·8 
9 ·8 
9·S 
9 ·8 
. I 
I 
~ 
. 
? 
o 
? 
1-3 
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o 
.... 
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...,-
o 
~ 
I-' 
z 
o 
cT 
(D 
...,. 
~ ... 
o 
CJ1 
o 
I-' 
-.:l 
T1l.BLE II 
Time Deflection Deflection dx tx 
fr om the of the dt --:a-sec. dt 
r ecord weight in./sec. / 2 in., sec . 
in. ; n. 
1.76 0 .000 0 .000 0 .00 350 
1.77 .002 . 012 3 ·75 350 
1. 78 •013 . 07'3 7 ·3 350 
1. 79 . 029 .174 11.2 372 
1.80 . 047 .282 15 ·3 450 
1.81 . 079 .474 21.2 668 
l .815 --- --- I --- 720 
1.82 . ll2 .672 28 · 5 665 
1.83 .167 1 . 000 34 .2 457 
1.84 .221 1·326 37 . 5 232 
1.85 .301 1.806 39 ·5 150 
1.86 
.364 2 .184 40 .8 122 
1.87 .443 2 . 658 42 .0 llO 
1.88 
· 515 3.090 43·0 llO 
tx ;:) d x + K x ;r-
dtZ M dt 
g g 
0 · 90 1. 90 
·90 1. 90 
·90 1.90 
·96 2 .00 
LIb 2 .30 
1.72 2 .85 
1.86 3 .05 
1. 72 2 ·95 
1.18 2 .47 
.60 2 .05 
I 
z 
>=-
. 
o 
l> 
1-3 
CD 
() 
P' 
~ 
f-J. 
() 
t'J 
I-' 
z 
o 
c+ 
CD 
z 
o 
CJ1 
o 
I-' 
co 
! . A.O .A. Technical Note No. 501 
-'Weight 
-- Ball bearing 
-Guide cylinder 
Section through 
guide cy11nder 
& weight 
1l0t or 
--/ ' __ I 
/ I 
,j i 
/ I 
I I 
I Mirror 
I 
I 
\ Light source 
\ 
\ 
-Film drum 
/,,-Pulleys / 
-- " / 
,/ 
,/ 
/ 
/P1nion 
/ ..--Rack 
./ 
-" 
....... 
..--
Spring -------- --- .... -" 
/ 
/ 
/ 
/ 
Fig . 1 
, 
Guide 
cylinder 
.... Weight 
>Ball 
bearings 
rig~re 1. - Diagrammatic sketch of landing-shock reoorder. 
N.A.C.A. Technical Note No.50l Fig. 2 
Figure 2.- Landing-shock recorder 
N.A .C.A. Technical Note No.50l 
Film motion 
Film motion 
Film motion 
Figs. 3,5a , 5b 
Fi gure 3 . -
Landing-
Ehock-
r eoorder 
1' 8 cord 
of vibrat-
ing beam. 
Figure 5a.-
Airplane 
landinS· 
Landing-
shock-
recorder 
record. 
Fi gure 5b ,-
Airplane 
landing. 
Standard 
aooeler-
ometer 
record 
200 1.00 
160 .80 
-g 
o .cI 
o 0 
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..-I 
o 
o 
...... 
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o 
..-I 
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~ 
.20 
o .005 .010 .015 • 020 
Time, second 
Figure 4.- Calculated curves from record of figure 3. 
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N.A.C.A. Technical Note No.501 
'ro ~Q) orllD 
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Total V V / ~ aooeleration / ~ , 
v 
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1.0 100 
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---1. 78 1.84 1. 80 1. 82 
Time, seconds 
rig. 8 
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dt:1. 
1.86 o 0 
Figure 6.- Ca1ou1ated ourves from reoord of figure Sa 


Landing-shock Recorder

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