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Author:Purokoski, Tero
Title:Stability of a towed cable-body system
Hinattavan kappaleen ja sen hinausköyden vakavuus
Publication type:Master's thesis
Publication year:2010
Pages:x + 147 s. + [43]      Language:   eng
Department/School:Sovelletun mekaniikan laitos
Main subject:Lentotekniikka   (Kul-34)
Supervisor:Soinne, Erkki
Instructor:Hoffren, Jaakko
OEVS:
Electronic archive copy is available via Aalto Thesis Database.
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Location:P1 Ark Aalto  3152   | Archive
Keywords:towed body
cable-body system
stability
steady state
dynamic analysis
hinattava kappale
hinausköyden ja kappaleen yhdistelmä
vakavuus
tasapainotila
dynaaminen analyysi
Abstract (eng): This thesis focuses on the dynamic stability of a towed cable-body system.
Such systems could be, for example, scientific instrumentation towed aerially by an aircraft or underwater vehicles towed behind a ship.
A mathematical model published by Etkin has been used as a basis for a computer program that calculates the steady state and subsequently the dynamic stability of the cable-body system.
The dynamic analysis is furthermore divided into longitudinal and lateral parts.
The equations of motion of the towed system are linearized by utilizing the small-disturbance theory.
The cable is modelled as a flexible and elastic one having internal damping, and it is treated in segments with multiple degrees of freedom.

The fundamental operation of the model was tested by applying it to different basic cases for which the exact solution is known.
Further testing was carried out by calculation of various steady-state cases.
Both aerial and underwater systems were used for comparisons.
These tests showed that the model calculates the steady-state shape and the tension of the cable very well.

To validate the calculation method of dynamic analysis, a pendant body towed by a cable attached to an aircraft was studied in detail.
The cable attachment point and tow speeds were varied and the results were compared to Etkin's results.
In case of lateral stability, the results are practically identical to those obtained by Etkin.
Also in the longitudinal case, the results are in good agreement with each other.
The dynamic analysis revealed that the cable-body system can be laterally unstable at a certain speed range.
However, this can be corrected by choosing a proper attachment point.
The importance of a proper attachment point became also evident in comprehensive parametric studies performed.
Abstract (fin): Tässä diplomityössä tutkitaan hinattavan kappaleen dynaamista vakavuutta.
Tällaisia hinattavia kappaleita ovat esimerkiksi lentokoneella hinattavat tieteelliset tutkimuslaitteet tai laivan perässä hinattavat vedenalaiset luotaimet.
Etkinin julkaisemaa matemaattista mallia on käytetty perustana tietokoneohjelmassa, joka laskee ensin hinattavan kappaleen tasapainotilan ja tämän jälkeen dynaamisen vakavuuden.
Dynaamisen vakavuuden laskenta on edelleen jaettu pitkittäiseen ja poikittaiseen osaan.
Hinausyhdistelmän liikeyhtälöt on linearisoitu käyttämällä hyväksi pienten häiriöiden teoriaa.
Hinausköysi on mallinnettu taipuisaksi ja venyväksi.
Laskennassa köysi jaetaan osiin, joilla on useita vapausasteita.
Köydellä voi olla sisäistä vaimennusta.

Mallin perustoiminta varmistettiin soveltamalla sitä yksinkertaistettuihin tapauksiin, joiden tarkka ratkaisu tunnettiin.
Tämän jälkeen siirryttiin laskemaan erilaisia tasapainotiloja.
Vertailuun käytettiin sekä ilmassa että vedessä hinattavia kappaleita.
Vertailujen tulokset osoittivat, että malli laskee hinausköyden muodon ja sen jännitykset tasapainotilassa tarkasti.

Dynaamisen analyysin laskenta todennettiin tutkimalla yksityiskohtaisesti lentokoneella hinattavaa ilmaa raskaampaa kappaletta.
Sekä hinausköyden kiinnityspistettä että lentonopeutta vaihdeltiin ja tuloksia verrattiin Etkinin saamiin tuloksiin.
Poikittaisen vakavuuden tapauksessa tulokset olivat käytännössä täsmälleen samat.
Myös pitkittäisen vakavuuden tulokset vastasivat hyvin toisiaan.
Dynaamisessa analyysissa havaittiin, että hinausyhdistelmä voi olla poikittaisessa suunnassa epävakaa äärellisellä nopeusalueella.
Tämä voidaan kuitenkin korjata sopivalla hinausköyden kiinnityspisteen valinnalla.
Tehdyt perusteelliset parametritarkastelut myös korostivat oikean kiinnityspisteen valinnan tärkeyttä.
ED:2010-10-26
INSSI record number: 41221
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