Share-Based Compensation (Schedule of Share-Based Compensation Expense) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2025	Aug. 31, 2024	Aug. 31, 2023
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	$ 8,236	$ 6,496	$ 6,698
Tax benefit	(1,699)	(1,527)	(1,574)
Share-based compensation expense, net of tax	6,537	4,969	5,124
Cost Of Operating Revenues [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	169	183	183
Engineering and Research [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	214	190	232
Selling [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	613	650	632
General and Administrative [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	7,240	5,473	5,651
Operating Expenses [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	$ 8,067	$ 6,313	$ 6,515