Employee Benefit Plan, Schedule, Asset Held for Investment (Details) - EBP0757636 - USD ($)	12 Months Ended
	Sep. 30, 2025	Sep. 30, 2024
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	$ 1,820,488,589	$ 1,647,194,422
EBP, Investment, Excluding Plan Interest in Master Trust, Contract Value	79,796,142	83,780,317
Notes receivable from participants	16,108,130	$ 14,681,980
EBP, Investment, Fair and Contract Value	1,916,392,861
Investment, Identifier [Axis]: BlackRock Lifepath Index 2030 Fund O
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	133,085,088
Investment, Identifier [Axis]: BlackRock Lifepath Index 2035 Fund O
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	126,232,864
Investment, Identifier [Axis]: BlackRock Lifepath Index 2040 Fund O
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	102,082,009
Investment, Identifier [Axis]: BlackRock Lifepath Index 2045 Fund O
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	99,275,642
Investment, Identifier [Axis]: BlackRock Lifepath Index 2050 Fund O
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	92,442,041
Investment, Identifier [Axis]: BlackRock Lifepath Index 2055 Fund O
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	69,681,551
Investment, Identifier [Axis]: BlackRock Lifepath Index 2060 Fund O
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	33,280,965
Investment, Identifier [Axis]: BlackRock Lifepath Index 2065 Fund O
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	15,014,912
Investment, Identifier [Axis]: BlackRock Lifepath Index Retirement Fund O
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	193,848,309
Investment, Identifier [Axis]: Capital Group Europacific Growth SA
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	24,810,312
Investment, Identifier [Axis]: JPMorgan Small Cap Value R6
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	9,956,523
Investment, Identifier [Axis]: Large Cap Growth JPMorgan Investment Management Fund
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	94,960,318
Investment, Identifier [Axis]: MFS Mid Cap Growth Class R6
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	15,286,697
Investment, Identifier [Axis]: Moog Inc. Class B Common Stock
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	369,929,005
Investment, Identifier [Axis]: New York Life Ins Co Anchor Account IV
EBP, Schedule of Asset Held for Investment [Line Items]
EBP, Investment, Excluding Plan Interest in Master Trust, Contract Value	79,796,142
Investment, Identifier [Axis]: Pimco Income Instl
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	31,071,405
Investment, Identifier [Axis]: Pimco Real Return Instl
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	11,617,364
Investment, Identifier [Axis]: T Rowe Price Integrated U.S. Small-Cap Growth Equity Inv
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	21,025,326
Investment, Identifier [Axis]: Vanguard Institutional Index Instl Pl
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	156,586,683
Investment, Identifier [Axis]: Vanguard Mid Cap Index Institutional
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	38,275,074
Investment, Identifier [Axis]: Vanguard Small Cap Index I
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	42,376,677
Investment, Identifier [Axis]: Vanguard Total Bond Market Index Institutional
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	46,720,874
Investment, Identifier [Axis]: Vanguard Total Intl Stock Index I
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	47,348,613
Investment, Identifier [Axis]: Vanguard Windsor Admiral
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	36,440,099
Investment, Identifier [Axis]: Victory Sycamore Established Value R6
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	9,140,238
Mutual Fund
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	465,845,573
EBP, Employer, Common Stock
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	369,929,005
EBP, Pooled Separate Account
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	119,770,630
Common Collective Trust
EBP, Schedule of Asset Held for Investment [Line Items]
Investments at fair value	$ 864,943,381
Minimum
EBP, Schedule of Asset Held for Investment [Line Items]
EBP, Asset Held for Investment, Participant Loan, Interest Rate	4.25%
Maximum
EBP, Schedule of Asset Held for Investment [Line Items]
EBP, Asset Held for Investment, Participant Loan, Interest Rate	9.50%