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Long-Term Debt, Finance Leases, and Other Borrowings - Schedule of Long-term Debt (Parenthetical) (Detail)
 12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
United Revolving Credit Facility Quaterly Collateralized By Underlying Equipment And Investments Through Two Thousand Twenty Eight [Member]    
Debt Instrument [Line Items]    
Debt instrument maturity year 2028 2028
Long term debt interest rate description quarterly interest based on SOFR plus interest spread at 4.50%  
United Revolving Credit Facility Quaterly Collateralized By Underlying Equipment And Investments Through Two Thousand Twenty Eight [Member] | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]    
Debt Instrument [Line Items]    
Long term debt, basis spread on variable rate 4.50%  
Senior and Subordinated Notes Payable to Secured Parties, Due in Monthly Installments Collateralized by the Underlying Aircraft Through 2027 [Member]    
Debt Instrument [Line Items]    
Debt instrument maturity year 2027 2027
Long term debt interest rate description due in monthly installments, interest based on SOFR plus interest spread at 2.71%  
Senior and Subordinated Notes Payable to Secured Parties, Due in Monthly Installments Collateralized by the Underlying Aircraft Through 2027 [Member] | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]    
Debt Instrument [Line Items]    
Long term debt, basis spread on variable rate 2.71%  
Notes Payable to Secured Parties, Due in Semi-annual Installments, Collateralized by the Underlying Aircraft Through 2028 [Member]    
Debt Instrument [Line Items]    
Debt instrument maturity year 2028 2028
Long term debt interest rate description due in semi-annual installments, interest based on fixed interest of 4.75% to 6.25% through 2028  
Notes Payable to Secured Parties, Due in Semi-annual Installments, Collateralized by the Underlying Aircraft Through 2028 [Member] | Minimum [Member] | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]    
Debt Instrument [Line Items]    
Long term debt, fixed interest rate 4.75%  
Notes Payable to Secured Parties, Due in Semi-annual Installments, Collateralized by the Underlying Aircraft Through 2028 [Member] | Maximum [Member] | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]    
Debt Instrument [Line Items]    
Long term debt, fixed interest rate 6.25%  
United Bridge Loan Quaterly Collateralized By Underlying Equipment And Investments Through Two Thousand Twenty Four [Member]    
Debt Instrument [Line Items]    
Long term debt interest rate description due in quarterly installments based on SOFR plus interest spread at 4.50%  
United Bridge Loan Quaterly Collateralized By Underlying Equipment And Investments Through Two Thousand Twenty Four [Member] | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]    
Debt Instrument [Line Items]    
Debt instrument maturity year 2024 2024
Long term debt, basis spread on variable rate 4.50%  
Other Obligations Due to Financial Institutions, Monthly or Quarterly Collateralized by the Underlying Equipment, Due 2022 Through 2027 [Member]    
Debt Instrument [Line Items]    
Long term debt interest rate description monthly and/or quarterly interest due from 2022 through 2027  
Other Obligations Due to Financial Institutions, Monthly or Quarterly Collateralized by the Underlying Equipment, Due 2022 Through 2027 [Member] | Minimum [Member]    
Debt Instrument [Line Items]    
Debt instrument maturity year 2022 2022
Other Obligations Due to Financial Institutions, Monthly or Quarterly Collateralized by the Underlying Equipment, Due 2022 Through 2027 [Member] | Maximum [Member]    
Debt Instrument [Line Items]    
Debt instrument maturity year 2027 2027
Notes Payable to Secured Parties, Due in Quarterly Installments Collateralized by the Underlying Aircraft Through 2028 [Member]    
Debt Instrument [Line Items]    
Debt instrument maturity year 2028 2028
Long term debt interest rate description due in quarterly installments, interest based on SOFR plus interest at spread 2.20% to 2.32% for senior note & 4.50% for subordinated note  
Notes Payable to Secured Parties, Due in Quarterly Installments Collateralized by the Underlying Aircraft Through 2028 [Member] | Senior Subordinated Notes [Member]    
Debt Instrument [Line Items]    
Long term debt, basis spread on variable rate 4.50%  
Notes Payable to Secured Parties, Due in Quarterly Installments Collateralized by the Underlying Aircraft Through 2028 [Member] | Minimum [Member] | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member] | Senior Notes [Member]    
Debt Instrument [Line Items]    
Long term debt, basis spread on variable rate 2.20%  
Notes Payable to Secured Parties, Due in Quarterly Installments Collateralized by the Underlying Aircraft Through 2028 [Member] | Maximum [Member] | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member] | Senior Notes [Member]    
Debt Instrument [Line Items]    
Long term debt, basis spread on variable rate 2.32%  
Notes Payable to Financial Institution, Due in Monthly Installments Collateralized by the Underlying Equipment, Through 2027 [Member]    
Debt Instrument [Line Items]    
Debt instrument maturity year 2027 2027
Long term debt interest rate description due in monthly installments, interest based on fixed interest of 7.50%, through 2027  
Notes Payable to Financial Institution, Due in Monthly Installments Collateralized by the Underlying Equipment, Through 2027 [Member] | LIBOR [Member]    
Debt Instrument [Line Items]    
Long term debt, basis spread on variable rate 7.50%  
Notes Payable To Financial Institution Due In Monthly Installments Collateralized By Underlying Equipment Through Two Thousand Twenty Four [Member]    
Debt Instrument [Line Items]    
Debt instrument maturity year 2024 2024
Long term debt interest rate description due in monthly installments, interest based on SOFR plus interest spread at 3.10%  
Notes Payable To Financial Institution Due In Monthly Installments Collateralized By Underlying Equipment Through Two Thousand Twenty Four [Member] | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]    
Debt Instrument [Line Items]    
Long term debt, basis spread on variable rate 3.10%  
Notes Payable to the UST, Quarterly Through 2025 [Member]    
Debt Instrument [Line Items]    
Debt instrument maturity year 2025 2025
Long term debt interest rate description Notes payable to the UST, quarterly interest based on SOFR plus interest spread at 3.50  
Notes Payable to the UST, Quarterly Through 2025 [Member] | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]    
Debt Instrument [Line Items]    
Long term debt, basis spread on variable rate 3.50%