{"id":1400,"date":"2021-07-12T00:55:05","date_gmt":"2021-07-12T05:55:05","guid":{"rendered":"https:\/\/charles-oneill.com\/blog\/?p=1400"},"modified":"2021-07-12T01:40:15","modified_gmt":"2021-07-12T06:40:15","slug":"turning-inbound","status":"publish","type":"post","link":"https:\/\/charles-oneill.com\/blog\/turning-inbound\/","title":{"rendered":"Turning Inbound: A mathematical solution"},"content":{"rendered":"\n

When should you start your turn inbound to exactly ensure the needle will be centered? This post explains and demonstrates a quick mental math solution. First, the answer:<\/p>\n\n\n\n

Begin your turn no later than the CDI dot corresponding to one-half of the angle to intercept divided by 3 and divided by the time to pass from one CDI dot to the next.<\/strong><\/p>\n\n\n\n

This solution works for turning inbound & outbound for tracking a VOR radial, a LOC\/ILS, or any situation where you can count intervals leading up to a desired track. <\/p>\n\n\n\n

Example<\/h2>\n\n\n\n

You are on a 45 degree intercept. The needle is alive and you count 4 seconds between CDI dots.<\/p>\n\n\n\n

\"\"<\/a><\/figure><\/div>\n\n\n\n

The mental math is: 45 divided by 3 is 15\u2026..\u00a0 15 divided by 4 is about 4\u2026. Half of 4 is 2. Turn no later than 2 dots.<\/em><\/p>\n\n\n\n

\"\"<\/a><\/figure><\/div>\n\n\n\n

Derivation:<\/h2>\n\n\n\n
\"\"<\/a><\/figure><\/div>\n\n\n\n

The pilot needs a quicker and more intuitive solution. We can simplify this engineering-style intercept equation with a few steps.<\/p>\n\n\n\n

\"\"<\/a><\/figure><\/div>\n\n\n\n

Thus the pilot solution in words is: Begin your turn no later than the CDI dot corresponding to one-half of the angle to intercept divided by 3 and divided by the time to pass from one CDI dot to the next<\/strong>. <\/p>\n\n\n\n

Experimentally Developed Solution:<\/h2>\n\n\n\n

Full disclosure: I did not initially develop this intercept solution based on the mathematics. Rather, I experimentally flew many intercepts and developed the following rule of thumb. By a complete stroke of luck, the experimental solution happens to be exactly identical to the mathematical solution above.<\/p>\n\n\n\n

\"\"<\/a><\/figure><\/div>\n\n\n\n

Disclaimer<\/h2>\n\n\n\n

This solution is only meant for intuition and the mathematical understanding of intercepts. You must <\/strong>follow ATC, the appropriate regulations and standard operating procedures when flying. Find and train with an instructor, preferably with a CFII. No exceptions!<\/p>\n","protected":false},"excerpt":{"rendered":"

When should you start your turn inbound to exactly ensure the needle will be centered? This post explains and demonstrates a quick mental math solution. First, the answer: Begin your turn no later than the CDI dot corresponding to one-half of the angle to intercept divided by 3 and divided by the time to pass […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[160],"tags":[],"_links":{"self":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts\/1400"}],"collection":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/comments?post=1400"}],"version-history":[{"count":16,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts\/1400\/revisions"}],"predecessor-version":[{"id":1422,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts\/1400\/revisions\/1422"}],"wp:attachment":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/media?parent=1400"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/categories?post=1400"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/tags?post=1400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}