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Share-Based Compensation (Schedule of Share-Based Compensation Expense) (Details) - USD ($) $ in Thousands | 12 Months Ended
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Aug. 31, 2021 | Aug. 31, 2020 | Aug. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Total share-based compensation expense | $ 6,528 | $ 5,847 | $ 4,395
Tax benefit | (1,534) | (1,374) | (1,033)
Share-based compensation expense, net of tax | 4,994 | 4,473 | 3,362
Cost Of Operating Revenues [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Total share-based compensation expense | 258 | 142 | 105
Engineering and Research [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Total share-based compensation expense | 202 | 207 | 221
Selling [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Total share-based compensation expense | 544 | 419 | 250
General and Administrative [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Total share-based compensation expense | 5,524 | 5,079 | 3,819
Operating Expenses [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Total share-based compensation expense | $ 6,270 | $ 5,705 | $ 4,290

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