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Financing Arrangements (Details) (USD $)
In Millions, unless otherwise specified
3 Months Ended 6 Months Ended
Nov. 30, 2014
Nov. 30, 2013
Nov. 30, 2014
Nov. 30, 2013
May 31, 2014
Financing Arrangements          
Total debt $ 635.3us-gaap_DebtLongtermAndShorttermCombinedAmount   $ 635.3us-gaap_DebtLongtermAndShorttermCombinedAmount   $ 634.0us-gaap_DebtLongtermAndShorttermCombinedAmount
Current maturities of debt (46.3)us-gaap_DebtCurrent   (46.3)us-gaap_DebtCurrent   (69.7)us-gaap_DebtCurrent
Long-term debt 589.0us-gaap_LongTermDebtNoncurrent   589.0us-gaap_LongTermDebtNoncurrent   564.3us-gaap_LongTermDebtNoncurrent
Amount of convertible notes repurchased 30.0us-gaap_DebtInstrumentRepurchasedFaceAmount   30.0us-gaap_DebtInstrumentRepurchasedFaceAmount    
Cash paid for convertible notes repurchased 31.1us-gaap_DebtInstrumentRepurchaseAmount   31.1us-gaap_DebtInstrumentRepurchaseAmount    
Accrued interest 1.1us-gaap_AccruedLiabilitiesCurrentAndNoncurrent   1.1us-gaap_AccruedLiabilitiesCurrentAndNoncurrent    
Interest expense          
Amortization of discount     1.4us-gaap_AmortizationOfDebtDiscountPremium 3.0us-gaap_AmortizationOfDebtDiscountPremium  
Revolving credit facility expiring April 24, 2018 with interest payable monthly          
Financing Arrangements          
Total debt 170.0us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_LineOfCreditMember
  170.0us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_LineOfCreditMember
  130.0us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_LineOfCreditMember
Secured credit facility (secured by aircraft and related engines and components) due April 23, 2015 with floating interest rate, payable monthly          
Financing Arrangements          
Total debt 25.3us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_LineOfCreditFacilityExpiring2015Member
  25.3us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_LineOfCreditFacilityExpiring2015Member
  29.9us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_LineOfCreditFacilityExpiring2015Member
Note payable due March 9, 2017 with floating interest rate, payable semi-annually on June 1 and December 1          
Financing Arrangements          
Total debt 25.0us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_NotesPayableDue2017Member
  25.0us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_NotesPayableDue2017Member
  30.0us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_NotesPayableDue2017Member
Notes payable due January 15, 2022 with interest at 7.25% payable semi-annually on January 15 and July 15          
Financing Arrangements          
Interest rate (as a percent) 7.25%us-gaap_DebtInstrumentInterestRateStatedPercentage
/ us-gaap_DebtInstrumentAxis
= air_NotesPayable7.25PercentDue2022Member
  7.25%us-gaap_DebtInstrumentInterestRateStatedPercentage
/ us-gaap_DebtInstrumentAxis
= air_NotesPayable7.25PercentDue2022Member
   
Total debt 332.2us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_NotesPayable7.25PercentDue2022Member
  332.2us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_NotesPayable7.25PercentDue2022Member
  332.6us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_NotesPayable7.25PercentDue2022Member
Convertible notes payable          
Financing Arrangements          
Carrying value of long-term debt 49.8us-gaap_DebtInstrumentCarryingAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
  49.8us-gaap_DebtInstrumentCarryingAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
  49.8us-gaap_DebtInstrumentCarryingAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
Long-term debt:          
Principal amount 49.8us-gaap_DebtInstrumentCarryingAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
  49.8us-gaap_DebtInstrumentCarryingAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
  49.8us-gaap_DebtInstrumentCarryingAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
Unamortized discount (3.0)us-gaap_DebtInstrumentUnamortizedDiscount
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
  (3.0)us-gaap_DebtInstrumentUnamortizedDiscount
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
  (4.1)us-gaap_DebtInstrumentUnamortizedDiscount
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
Net carrying amount 46.8us-gaap_LongTermDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
  46.8us-gaap_LongTermDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
  45.7us-gaap_LongTermDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
Equity component, net of tax 20.6us-gaap_DebtInstrumentConvertibleCarryingAmountOfTheEquityComponent
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
  20.6us-gaap_DebtInstrumentConvertibleCarryingAmountOfTheEquityComponent
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
  20.6us-gaap_DebtInstrumentConvertibleCarryingAmountOfTheEquityComponent
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
Interest expense          
Coupon interest 0.4us-gaap_InterestExpenseDebtExcludingAmortization
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
0.9us-gaap_InterestExpenseDebtExcludingAmortization
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
0.9us-gaap_InterestExpenseDebtExcludingAmortization
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
1.7us-gaap_InterestExpenseDebtExcludingAmortization
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
 
Amortization of deferred financing fees   0.1us-gaap_AmortizationOfFinancingCosts
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
0.1us-gaap_AmortizationOfFinancingCosts
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
0.2us-gaap_AmortizationOfFinancingCosts
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
 
Amortization of discount 0.6us-gaap_AmortizationOfDebtDiscountPremium
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
1.5us-gaap_AmortizationOfDebtDiscountPremium
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
1.3us-gaap_AmortizationOfDebtDiscountPremium
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
2.9us-gaap_AmortizationOfDebtDiscountPremium
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
 
Interest expense related to convertible notes 1.0us-gaap_InterestExpenseDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
2.5us-gaap_InterestExpenseDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
2.3us-gaap_InterestExpenseDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
4.8us-gaap_InterestExpenseDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleNotesPayableMember
 
Convertible notes payable due February 1, 2015 with interest at 1.75% payable semi-annually on February 1 and August 1          
Financing Arrangements          
Interest rate (as a percent) 1.75%us-gaap_DebtInstrumentInterestRateStatedPercentage
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable1.75PercentDue2015Member
  1.75%us-gaap_DebtInstrumentInterestRateStatedPercentage
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable1.75PercentDue2015Member
   
Long-term debt:          
Net carrying amount 0us-gaap_LongTermDebt
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable1.75PercentDue2015Member
  0us-gaap_LongTermDebt
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable1.75PercentDue2015Member
  29.8us-gaap_LongTermDebt
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable1.75PercentDue2015Member
Convertible notes payable due March 1, 2016 with interest at 2.25% payable semi-annually on March 1 and September 1          
Financing Arrangements          
Interest rate (as a percent) 2.25%us-gaap_DebtInstrumentInterestRateStatedPercentage
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable2.25PercentDue2016Member
  2.25%us-gaap_DebtInstrumentInterestRateStatedPercentage
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable2.25PercentDue2016Member
   
Total debt 46.8us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable2.25PercentDue2016Member
  46.8us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable2.25PercentDue2016Member
  45.7us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable2.25PercentDue2016Member
Long-term debt:          
Effective interest rate (as a Percent) 7.41%us-gaap_DebtInstrumentInterestRateEffectivePercentage
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable2.25PercentDue2016Member
  7.41%us-gaap_DebtInstrumentInterestRateEffectivePercentage
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable2.25PercentDue2016Member
   
Convertible notes payable due February 1, 2026 with interest at 1.75% payable semi-annually on February 1 and August 1          
Long-term debt:          
Effective interest rate (as a Percent) 7.41%us-gaap_DebtInstrumentInterestRateEffectivePercentage
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable1.75PercentDue2026Member
  7.41%us-gaap_DebtInstrumentInterestRateEffectivePercentage
/ us-gaap_DebtInstrumentAxis
= air_ConvertibleNotesPayable1.75PercentDue2026Member
   
7.25% bonds, 1.75% and 2.25% convertible notes          
Financing Arrangements          
Carrying value of long-term debt 379.0us-gaap_DebtInstrumentCarryingAmount
/ us-gaap_DebtInstrumentAxis
= air_NotesPayable7.25PercentAndConvertibleNotesPayable1.75And2.25PercentMember
  379.0us-gaap_DebtInstrumentCarryingAmount
/ us-gaap_DebtInstrumentAxis
= air_NotesPayable7.25PercentAndConvertibleNotesPayable1.75And2.25PercentMember
   
Long-term debt:          
Principal amount 379.0us-gaap_DebtInstrumentCarryingAmount
/ us-gaap_DebtInstrumentAxis
= air_NotesPayable7.25PercentAndConvertibleNotesPayable1.75And2.25PercentMember
  379.0us-gaap_DebtInstrumentCarryingAmount
/ us-gaap_DebtInstrumentAxis
= air_NotesPayable7.25PercentAndConvertibleNotesPayable1.75And2.25PercentMember
   
7.25% bonds, 1.75% and 2.25% convertible notes | Significant other observable inputs (Level 2)          
Financing Arrangements          
Estimated fair value of long-term debt 402.2us-gaap_LongTermDebtFairValue
/ us-gaap_DebtInstrumentAxis
= air_NotesPayable7.25PercentAndConvertibleNotesPayable1.75And2.25PercentMember
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
  402.2us-gaap_LongTermDebtFairValue
/ us-gaap_DebtInstrumentAxis
= air_NotesPayable7.25PercentAndConvertibleNotesPayable1.75And2.25PercentMember
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
   
Remaining variable rate and fixed rate debt | Significant other unobservable inputs (Level 3)          
Financing Arrangements          
Estimated fair value of long-term debt 256.3us-gaap_LongTermDebtFairValue
/ us-gaap_DebtInstrumentAxis
= air_RemainingVariableAndFixedRateDebtMember
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
  256.3us-gaap_LongTermDebtFairValue
/ us-gaap_DebtInstrumentAxis
= air_RemainingVariableAndFixedRateDebtMember
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
   
Mortgage loan (secured by Wood Dale, Illinois facility) due August 1, 2015 with interest at 5.01%          
Long-term debt:          
Net carrying amount 11.0us-gaap_LongTermDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_MortgagesMember
  11.0us-gaap_LongTermDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_MortgagesMember
  11.0us-gaap_LongTermDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_MortgagesMember
Industrial revenue bond (secured by property, plant and equipment) due August 1, 2018          
Long-term debt:          
Net carrying amount 25.0us-gaap_LongTermDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_BondsMember
  25.0us-gaap_LongTermDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_BondsMember
  25.0us-gaap_LongTermDebt
/ us-gaap_DebtInstrumentAxis
= us-gaap_BondsMember
Other          
Financing Arrangements          
Total debt $ 36.0us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_OtherRecourseDebtMember
  $ 36.0us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_OtherRecourseDebtMember
  $ 65.8us-gaap_DebtLongtermAndShorttermCombinedAmount
/ us-gaap_DebtInstrumentAxis
= air_OtherRecourseDebtMember