?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F102%2F&rft.title=Height-volume+characteristics+of+a+fuel+tank&rft.creator=Budd%2C+Chris&rft.subject=Aerospace+and+defence&rft.description=A+key+feature+of+any+aircraft+is+its+fuel+system.+Fuel+is+stored+in+large+tanks+(typically+within+the+wing+of+the+aircraft)+which+are+approximately+rectangular%2C+but+have+detailed+internal+structure.+A+typical+tank+is+illustrated+in+Figure+1%2C+in+which+we+can+see+the+internal+stringers+and+other+small+details.%0A%0AFigure+1%3A+An+example+of+a+typical+fuel+tank+showing+the+internal+structures+including+corners+and+stringers.%0A%0AA+key+aspect+of+aircraft+safety+is+an+accurate+measurement+of+the+amount+of+fuel+in+the+tank.+To+determine+this%2C+the+height+h+of+the+fuel+at+certain+points+within+the+tank+is+measured+and+the+fuel+volume+V+is+determined+from+this.+However+the+relationship+between+height+and+volume+depends+crucially+on+the+pitch+angle%2C+%CE%B1%2C+and+roll+angle%2C+%CE%B2%2C+of+the+tank.+(This+is+clear+to+all+of+us+when+we+drive+a+car+and+see+that+the+indicated+fuel+level+in+the+tank+depends+upon+whether+we+are+going+up+or+down+hill+at+the+time.)+At+present+Airbus+uses+lookup+tables+to+link+height+to+volume+for+a+set+of+pitch+and+roll+angles.+As+the+fuel+tanks+become+more+and+more+intricate%2C+the+huge+amount+of+data+required+becomes+an+issue.+The+problem+posed+to+the+Study+Group+was+whether+the+lookup+tables+can+be+replaced+by+suitable+functions.+(Note+that+we+only+considered+the+static+problem%2C+which+assumed+that+the+fuel+was+in+equilibrium.+The+much+harder+problem+of+determining+the+volume+of+a+sloshing+fuel+was+not+considered%2C+but+might+make+a+very+interesting+problem+for+a+future+Study+Group.)%0A%0ATo+solve+this+problem+we+require+a+combination+of+numerical+analysis+and+geometry.+Numerical+methods+are+needed+to+determine+suitable+approximations+to+the+h-V+function.+However%2C+generating+such+approximations+turns+out+to+be+very+subtle%2C+because+of+the+way+that+the+fuel+interacts+with+the+tank+geometry.+This+leads+to+h-V+curves+which+are+nonsmooth+and+have+to+be+approximated+very+carefully.+An+understanding+of+the+way+that+this+nonsmoothness+arises+and+how+the+resulting+curves+can+be+approximated+forms+the+basis+of+this+Study+Group+report.&rft.date=2007-04-17&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F102%2F1%2FAirbus-FuelTanks.pdf&rft.identifier=++Budd%2C+Chris++(2007)+Height-volume+characteristics+of+a+fuel+tank.++%5BStudy+Group+Report%5D+++++