LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZULyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZQNiZGUkZVRlgvRmVuUSVhdXRvRictRiw2JVEqaW50ZXJmYWNlRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEsdHlwZXNldHRpbmdGJ0YvRjItRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRiw2JVEpZXh0ZW5kZWRGJ0YvRjJGOUY1LUYsNiNRIUYnprint(); # input placeholderJSFH
<Text-field style="Heading 1" layout="Heading 1">Introduction to the lateral plane</Text-field>At first, let us compare between the longitudinal plane to the lateral plane:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Longitudinal planeLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Lateral planeForcesLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=The forces equation are in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= direction.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=The forces equation is in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= direction.MomentLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= - Pitching momentLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= - Rolling momentLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= - Yawing momentSteeringLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EtYCZkZWx0YTtfX2VgRictSSNtb0dGJDYtUSJ+RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctRjA2LVEiLEYnRjNGNi9GOlEldHJ1ZUYnRjtGPUY/RkFGQ0ZFL0ZJUSwwLjMzMzMzMzNlbUYnRi8tRiw2I1EtYCZkZWx0YTtfX3RgRidGMw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EtYCZkZWx0YTtfX2FgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn - Aileron, contribute to the Rolling.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EtYCZkZWx0YTtfX3JgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn - Rader, contribute to the yawingVelocityLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEid0YnRi9GMkY5LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=Angular velocityLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiVkYnRi9GMkY5
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=From the table above it can be seen that we have only one forces equation in the lateral plane but two moment equations.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy - defined is the direction that the wind comes from.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHlfXzBgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn - The body contribution (most of the times it can be neglectable).In this course we assume that the wind flow that one side of the aircraft see is the same as the other side see when we have LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy. The side lift contribution is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYENfX3ZgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn: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Where 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 . In Maple we define 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we define:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbWlHRiQ2I1EuYENfX3ksJmJldGE7YEYnLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUYwNi1RKiZ1bWludXMwO0YnRjNGNkY5RjtGPUY/RkFGQy9GRlEsMC4yMjIyMjIyZW1GJy9GSUZOLUYsNiNRK2AmZXRhO19fdmBGJy1GMDYtUScmc2RvdDtGJ0YzRjZGOUY7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklGVy1JJm1mcmFjR0YkNigtRiw2I1EnYFNfX3ZgRictRiM2JC1GLDYjUSlgU19fcmVmYEYnRjMvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmNvLyUpYmV2ZWxsZWRHRjhGUy1GLDYjUThgQ19fTCxfX0xfXywmYWxwaGE7X192YEYnRlMtSShtZmVuY2VkR0YkNiQtRiM2Ji1JI21uR0YkNiRGYG9GMy1GMDYtUSgmbWludXM7RidGM0Y2RjlGO0Y9Rj9GQUZDRk1GTy1GLDYjUTJgJnNpZ21hO19fJmJldGE7YEYnRjNGMy1GLDYjUSFGJy1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0ZXLyUmZGVwdGhHRmFxLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUYsNiNROGBDX195LF9feV9fLCZkZWx0YTtfX3JgRidGLy1GIzYoRlBGU0ZZRlMtRiw2I1E4YENfX0wsX19MX18sJmRlbHRhO19fcmBGJ0YzRmlwRjM=And we get the side force equation: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When having LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NDY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj5GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjBGJ0YyRjI= we ask for positive moment that will "fix" the moment created by LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy , Hence, the condition for lateral static stability is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EuYENfX04sJmJldGE7YEYnLUkjbW9HRiQ2L1EiPkYnLyUrYmFja2dyb3VuZEdRLFsyNTUsMjU1LDBdRicvJSdvcGFxdWVHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk0tSSNtbkdGJDYmUSIwRidGM0Y2RjlGM0Y2Rjk=.The main side force is from the tail, hence LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EtYCZkZWx0YTtfX3JgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn generate moment that ease us overcome the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy moment and that is why it is easier to get the stability condition.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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
<Text-field style="Heading 1" layout="Heading 1">Exercise</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Given an aircraft with two engines and two vertical tails (as it shown in the figure below)-%'CANVASG6'-%)BOUNDS_XG6#,$-%&FloatG6#%)infinityG!""-%)BOUNDS_YGF'-%-BOUNDS_WIDTHG6#$"%giF--%.BOUNDS_HEIGHTG6#$"%g_F--%)CHILDRENG6/-%%OVALG6'-%(OUTLINEG6#-%&COLORG6&%$RGBG$""!F-FGFG-%/LINE_THICKNESSG6#$"#5F--%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$FGFG-%'ORIGING6#-%&POINTG6$$"%+IF-$"%&p#F--%&SCALEG6#-FU6$FLFL-%)ROTATIONG6#FG-%*LINESTYLEG6#FH-%%DATAG6%7$$"%SEF-$"$!eF-7$$"$?(F-$"%IUF-%'CLOSEDG-%%LINEG6'F@FI-FO6&FQ-FX6#-Fen6$$"%&["F-$"%bAF-F[oF`oFco-Fgo6&7$$"%!o#F-$"%+=F-7$$"$!HF-$"%+@F-7$$")/%35$!"'$"%!p#F-7$$"(K)RE!"%$"%5FF--Fep6'F@FI-FO6&FQ-FX6#-Fen6$$"%DXF-$"%lAF-F[oF`oFco-Fgo6&7$$"%SLF-$"%5=F-7$$"%+dF-$"%5@F-7$$"%5dF-$"%?FF-7$$"%!Q$F-Fdt-Fep6'F@FI-FO6&FQ-FX6#-Fen6$$"%+CF-$"%&e%F-F[oF`oFco-Fgo6&7$$"%!y#F-$"%qVF-7$$"%!z"F-$"%5XF-7$F]v$"%+[F-7$$"%5IF-Fbv-Fep6'F@FI-FO6&FQ-FX6#-Fen6$$"%:OF-$"%&f%F-F[oF`oFco-Fgo6&7$$"%?KF-$"%!Q%F-7$$"%5UF-F_v7$$"%?UF-$"%5[F-7$FevF`x-F>6'F@FI-FO6&FQ-FX6#-Fen6$$"%l5F-$"%!Q#F-F[oF`oFco-Fgo6%7$$"$I*F-$"%q=F-7$$"$q#F-$"%?5F-Fcp-F>6'F@FI-FO6&FQ-FX6#-Fen6$$"%X\F-$"%5CF-F[oF`oFco-Fgo6%7$F`x$"%+>F-FfyFcp-Fep6'F@-FJ6#$"#gF--FO6&FQ-FX6#-Fen6$F_q$"%DYF-F[oF`oFco-Fgo6$7$$"%]AF-$"%SWF-7$$"%gAF-F`x-Fep6'F@F^[l-FO6&FQ-FX6#-Fen6$$"%lPF-$"%NYF-F[oF`oFco-Fgo6$7$$"%gPF-$"%]WF-7$$"%qPF-$"%?[F--Fep6(F@-%/LINE_END_ARROWG6#Q*vee-arrow6"-FJ6#$"#:F--FO6&FQ-FX6#-Fen6$$"%0IF-$"%N8F-F[oF`o-Fdo6#""%-Fgo6$7$FgnFez7$Fgn$"$g#F--Fep6(F@F^^lFc^l-FO6&FQ-FX6#-Fen6$$"%IXF-$"%0CF-F[oF`oFa_l-Fgo6$Ff_l7$$"%ggF-Fau-%/TEXT_CONTAINERG6(Fc^l-FO6&FQ-FX6#-Fen6$$"%vKF-$"$I&F-F[oF`o-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTGFjal-Fgo6%7$$"%!3$F-$"$]$F-7$$"$!RF-$"$g$F-Fcp-%*PARAGRAPHG6#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Fb^l-F\al6(Fc^l-FO6&FQ-FX6#-Fen6$$"%vfF-FarF[oF`oFhalF\bl-Fgo6%7$$"%!y&F-$"%?DF-7$Ffbl$"$S$F-Fcp-F[cl6#Q[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given aircraft data:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Art 1</Text-field>Find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EuYENfX04sJmJldGE7YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== and determine if the aircraft is stable or not. Also find the lateral neutral point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EpYE5fX2xhdGBGJy1JI21vR0YkNi1RKCZtaW51cztGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGRy1GLDYjUShgeF9fY2dgRidGMw== .LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 3" layout="Heading 3">Solution</Text-field>In order to find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EuYENfX04sJmJldGE7YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== we will find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EuYENfX3ksJmJldGE7YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== and multiply by the distance.Note that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EuYENfX3ksJmJldGE7YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== is the side force generate from the engines and tails (v) contribution:QyY+SS9DX195LCZiZXRhO19fdkc2IiosSSkmZXRhO19fdkdGJSIiIkklU19fdkdGJUYoSSVTX193R0YlISIiSTBDX19MLCZhbHBoYTtfX3ZHRiVGKCwmRihGKEkwJnNpZ21hO19fJmJldGE7R0YlRitGKEYrPkk0Q19feSwmYmV0YTtfX2VuZ2luZUdGJSoqSSpTX19lbmdpbmVHRiVGKEYqRitJLiZldGE7X19lbmdpbmVHRiVGKEkyQ19feSwmYmV0YTtfX3Byb3BHRiVGKEYrprint(); # input placeholderTherefore, the total side force (multiplying by two because we have two engines and two vertical tails):print(); # input placeholderQyQ+SSRlcTFHNiIvSSxDX195LCZiZXRhO0dGJSwmSTRDX195LCZiZXRhO19fZW5naW5lR0YlIiIjSS9DX195LCZiZXRhO19fdkdGJSEiIyEiIg==print(); # input placeholderSo now we can find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EuYENfX04sJmJldGE7YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== :QyQ+SSRlcTJHNiIvSSxDX19OLCZiZXRhO0dGJSwmKihJNENfX3ksJmJldGE7X19lbmdpbmVHRiUiIiJJK3hfX3Byb3AtY2dHRiVGK0kiYkdGJSEiIiIiIy1JIipHJSpwcm90ZWN0ZWRHNiQsJEkvQ19feSwmYmV0YTtfX3ZHRiVGLywkKiZJKHhfX2NnLXZHRiVGK0YtRi5GLkYuRi4=print(); # input placeholderWe got that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EuYENfX04sJmJldGE7YEYnLUkjbW9HRiQ2LVEiPkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbW5HRiQ2JFEiMEYnRjNGMw== and therefore we can say that the aircraft is stable.In order to find the neutral point we use the following equation:QyQ+SSRlcTNHNiIvSSxDX19OLCZiZXRhO0dGJSooSSxDX195LCZiZXRhO0dGJSIiIiwmSSdOX19sYXRHRiVGKkkmeF9fY2dHRiUhIiJGKkkiYkdGJUYuRi4=print(); # input placeholderJSFH
So the neutral point is:LUkoaXNvbGF0ZUc2IjYkLUklc3Vic0clKnByb3RlY3RlZEc2JS9JLENfX04sJmJldGE7R0YkLUkkcmhzR0YoNiNJJGVxMkdGJC9JLENfX3ksJmJldGE7R0YkLUYtNiNJJGVxMUdGJC1JKGFsZ3N1YnNHRiQ2JC8qJiwmSSdOX19sYXRHRiQiIiJJJnhfX2NnR0YkISIiRjxJImJHRiRGPkkseF9fTi5sYXQtY2dHRiRJJGVxM0dGJEZAprint(); # input placeholder
JSFH
<Text-field style="Heading 2" layout="Heading 2">Art 2</Text-field>Find the maximal sideslip angle that possible in straight and level flight (take in consideration the pilot forces and rader limitation ).
<Text-field style="Heading 3" layout="Heading 3">Solution</Text-field>In this question we have two limitations for maximal sideslip angle: rader limitation - LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1ExYCZkZWx0YTtfX3IsbWF4YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==pilot forces limitation - LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EpYE1fX21heGBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=Note that the pilot need to handle the vertical tail with his own feet. The force on the rader is a function of the velocity. In low velocity the force in not too large and the pilot can handle it (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EtYCZkZWx0YTtfX3JgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1ExYCZkZWx0YTtfX3IsbWF4YEYnRjM=) and we will get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EuYCZiZXRhO19fbWF4YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== . In high velocity the pilot can not handle the rader and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EtYCZkZWx0YTtfX3JgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn is smaller than LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1ExYCZkZWx0YTtfX3IsbWF4YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== and we wont get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EuYCZiZXRhO19fbWF4YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== .
rader limitationLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=pilot force limitationWe write the yawing moment equation:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=QyQ+SSRlcTRHNiIvSSVDX19OR0YlLCYqJkklYmV0YUdGJSIiIkksQ19fTiwmYmV0YTtHRiVGK0YrKiZJKyZkZWx0YTtfX3JHRiVGK0kwQ19fTiwmZGVsdGE7X19yR0YlRitGKyEiIg==print(); # input placeholderThe expression for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1E4YENfX04sX19OX18sJmRlbHRhO19fcmBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= is from the two raders:PkkwQ19fTiwmZGVsdGE7X19yRzYiLCQqLkkuU19fJmRlbHRhO19fckdGJCIiIkklU19fd0dGJCEiIkkpJmV0YTtfX3ZHRiRGKEkwQ19fTCwmZGVsdGE7X19yR0YkRihJMXhfX2NnLSZkZWx0YTtfX3JHRiRGKEkiYkdGJEYqISIj = print(); # input placeholderIn order to get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EuYCZiZXRhO19fbWF4YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== we set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYENfX05gRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtbkdGJDYkUSIwRidGM0Yz and get:LUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMtSShpc29sYXRlRzYkRiRJKF9zeXNsaWJHNiI2JC1JJXN1YnNHRiQ2Jy9JJUNfX05HRioiIiEvSSViZXRhR0YqSTcmYmV0YTtfX21heCwmZGVsdGE7X19yR0YqL0krJmRlbHRhO19fckdGKkkvJmRlbHRhO19fcixtYXhHRiovSSxDX19OLCZiZXRhO0dGKi1JJHJoc0dGJDYjSSRlcTJHRipJJGVxNEdGKkY0print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Now we will find the pilot force limitation:QyQ+SSdNX19tYXhHNiIqJkktRl9fcGlsb3QsbWF4R0YlIiIiSSVHX19yR0YlISIiRio=print(); # input placeholderThe moment is:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=QyQ+SSRlcTVHNiIvSSdNX19tYXhHRiUqKC1JIipHJSpwcm90ZWN0ZWRHNiQsJCoqSSRyaG9HRiUiIiJJInZHRiUiIiNJLlNfXyZkZWx0YTtfX3JHRiVGMEkpQ19faCxtYXhHRiVGMCNGMEYyRjJGMEkpJmV0YTtfX3ZHRiVGMEkuY19fJmRlbHRhO19fckdGJUYwISIiNow we need to find the expression for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1ErYENfX2gsbWF4YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== :QyQ+SSRlcTZHNiIvSSlDX19oLG1heEdGJSwoKiZJKyZkZWx0YTtfX3JHRiUiIiJJMENfX2gsJmRlbHRhO19fckdGJUYrRisqJkksQ19faCwmYmV0YTtHRiVGK0kyJmJldGE7X19tYXgscGlsb3RHRiVGK0YrSSZDX19oMEdGJUYrISIiprint(); # input placeholderIn order to find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy we need to find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EtYCZkZWx0YTtfX3JgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn using the yawing moment expression:JSFHQyQ+SSRlcTdHNiIvSSVDX19OR0YlLCYqJkkrJmRlbHRhO19fckdGJSIiIkkwQ19fTiwmZGVsdGE7X19yR0YlRitGKyomSSxDX19OLCZiZXRhO0dGJUYrSTImYmV0YTtfX21heCxwaWxvdEdGJUYrRishIiI=We ask for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYENfX05gRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtbkdGJDYkUSIwRidGM0Yz and isolate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EtYCZkZWx0YTtfX3JgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn :LUkoaXNvbGF0ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUklc3Vic0dGJTYlL0klQ19fTkdGJyIiIS9JLENfX04sJmJldGE7R0YnLUkkcmhzR0YlNiNJJGVxMkdGJ0kkZXE3R0YnSSsmZGVsdGE7X19yR0Ynprint(); # input placeholderLUknYXNzaWduRyUqcHJvdGVjdGVkRzYjL0krJmRlbHRhO19fckc2IiwkSTImYmV0YTtfX21heCxwaWxvdEdGKCQiK1RZaHQ1ISIqSo now we can find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1ErYENfX2gsbWF4YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== :SSRlcTZHNiI=print(); # input placeholderLUknYXNzaWduRyUqcHJvdGVjdGVkRzYjL0kpQ19faCxtYXhHNiIsJEkyJmJldGE7X19tYXgscGlsb3RHRigkISt4SkRtOSEiKg==And now we can find the maximal sideslip angle under the moment the pilot can generate limitation:LUkoaXNvbGF0ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkSSRlcTVHRidJMiZiZXRhO19fbWF4LHBpbG90R0Ynprint(); # input placeholderJSFH
JSFH
As we can see, the maximal sideslip angle is a function of the velocity.For small velocity, the sideslip angle is constant and equal to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEmMC40MDZGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGLw== rad.For high velocity the sideslip angle is decreasing as we rise the velocity.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Art 3</Text-field>During the takeoff (at the rotation stage) the right engine stopped working. Does the aircraft can takeoff for 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 , without side force and in straight flight? In order to answer the question above find the minimal velocity that required to the limitations above, and compare it with the takeoff velocity.JSFH
<Text-field style="Heading 3" layout="Heading 3">Solution</Text-field>QyYtSSl1bmFzc2lnbkc2IjYjLkkrJmRlbHRhO19fckdGJSEiIi1GJDYjLkkpQ19faCxtYXhHRiVGKQ==Now we are in the conditions of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1ExYCZkZWx0YTtfX3IsbWF4YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== only now we have only one engine, hence, we have yawing moment. QyQ+SSZDX19OMEc2IiooSSVDX19UR0YlIiIiSSkmRGVsdGE7eUdGJUYoSSJiR0YlISIiRis=Side force expression: QyQ+SSRlcTdHNiIvSSVDX195R0YlLCYqJkklYmV0YUdGJSIiIkksQ19feSwmYmV0YTtHRiVGK0YrKiZJKyZkZWx0YTtfX3JHRiVGK0kwQ19feSwmZGVsdGE7X19yR0YlRitGKyEiIg==Without side force : LUklc3Vic0clKnByb3RlY3RlZEc2JC9JJUNfX3lHNiIiIiFJJGVxN0dGKA==print(); # input placeholderWe will find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EuYENfX3ksJmJldGE7YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== ( Note that now we have only one engine )QyQ+SSRlcThHNiIvSSxDX195LCZiZXRhO0dGJSwmSTRDX195LCZiZXRhO19fZW5naW5lR0YlIiIiSS9DX195LCZiZXRhO19fdkdGJSEiIyEiIg==print(); # input placeholderAnd the expression for JSFHPkkwQ19feSwmZGVsdGE7X19yRzYiLCQqKkkuU19fJmRlbHRhO19fckdGJCIiIkklU19fd0dGJCEiIkkpJmV0YTtfX3ZHRiRGKEkwQ19fTCwmZGVsdGE7X19yR0YkRighIiM=print(); # input placeholderTherefore, JSFHLUkoaXNvbGF0ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUklc3Vic0dGJTYnL0klYmV0YUdGJ0ksJmJldGE7X19tYXhHRicvSSsmZGVsdGE7X19yR0YnSS8mZGVsdGE7X19yLG1heEdGJy9JLENfX3ksJmJldGE7R0YnLUkkcmhzR0YlNiNJJGVxOEdGJy9JJUNfX3lHRiciIiFJJGVxN0dGJ0Yuprint(); # input placeholderNOTE:The sideslip angle should be positive! there is an error with the given data. JSFHNow we will write the yawing moment equation:QyQ+SSRlcTlHNiIvSSVDX19OR0YlLCgqJkksJmJldGE7X19tYXhHRiUiIiJJLENfX04sJmJldGE7R0YlRitGKyomSS8mZGVsdGE7X19yLG1heEdGJUYrSTBDX19OLCZkZWx0YTtfX3JHRiVGK0YrSSZDX19OMEdGJUYrISIiFor straight and level flight we will ask for QyQ+SSVDX19ORzYiIiIhISIiQyQ+SSxDX19OLCZiZXRhO0c2Ii1JJHJoc0clKnByb3RlY3RlZEc2I0kkZXEyR0YlISIiThe engine thrust:QyQ+SSJURzYiKiZJMVBfX3NpbmdsZX5lbmdpbmVHRiUiIiJJInZHRiUhIiJGKg==print(); # input placeholderQyQ+SSVDX19URzYiKiZJIlRHRiUiIiItSSIvRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJCooSSRyaG9HRiVGKEkidkdGJSIiI0klU19fd0dGJUYoI0YoRjNGKCEiIg==print(); # input placeholderIsolating the velocity:QyQ+SSJWRzYiLUkkcmhzRyUqcHJvdGVjdGVkRzYjLUkoaXNvbGF0ZUc2JEYoSShfc3lzbGliR0YlNiQtSSVldmFsR0YoNiRJJGVxOUdGJS9JLCZiZXRhO19fbWF4R0YlLUYnNiMvSTcmYmV0YTtfX21heCwmZGVsdGE7X19yR0YlJCIrQUY5a1MhIzVJInZHRiUhIiI=print(); # input placeholderWe got the limit velocity for which the pilot can flight with maximal sideslip angle.The takeoff velocity is:QyQ+SSVlcTEwRzYiLywkKipJJHJob0dGJSIiIkkidkdGJSIiI0klU19fd0dGJUYqSS1DX19MLFRha2VPZmZHRiVGKiNGKkYsSSJtR0YlISIiprint(); # input placeholderPkkrVl9fVGFrZU9mZkc2Ii1JJHJoc0clKnByb3RlY3RlZEc2Iy1JJmV2YWxmR0YnNiMtSShpc29sYXRlRzYkRidJKF9zeXNsaWJHRiQ2JEklZXExMEdGJEkidkdGJA==print(); # input placeholderJSFH
As we increase the velocity above the limit velocity the pilot will have to work easier. That is why the situation above is possible.