[Aus-soaring] Maths and rope breaks
I was by no way suggesting that one does the maths whilst in flight. It is used as the justification for performing such manoevures! Ok, radius of turn is given by R=V*V/(g*tan(bank)) R is radius in metres V is given in metres per second g is acceleration due gravity = 9.81 m/s/s Bank = angle of bank (AOB) in degrees (0=level) To convert knots to metres per second use: Airspeed in knots * 0.515 =metres/second. Given an example sink rate (i.e Bergfalke IV) at zero angle of bank at 60 KIAS as -3m/s (almost 600fpm down), making an approximation that the sink rate for a particular angle of bank is = 1/cos(bank). So at 30 degree AOB, the sink rate is -3.5m/s At 45 degree AOB, the sink rate is -4.2m/s At 60 degree AOB, the sink rate is -6 Hence pluging in values: At an airspeed of 60 knots AOB = 30, radius of turn is 552 feet = circling diameter of 336 metres AOB 45, radius = 319 feet, = circling diameter of 194 metres AOB 60, radius = 184 feet, = circling diameter of 112 metres The distance to travel half way around these circels (180 degree turn) is pi * diameter, time required to go the distance is distance travelled / airspeed AOB=30, distance=529m, time required=17secs, height loss (at sink of 3.5m/s) = 194 feet, diameter 336m AOB=45, distance=305m, time required=10secs, height loss (at sink of 4.2m/s) = 137 feet, diameter 194m AOB=60, distance=176m, time required=6secs, height loss (at sink of 6m/s) = 112 feet, diameter 112m Remember that the wider the diameter of the turn, you will have to turn through more than 180 degrees to get back to the strip, because the shallower turn will carry you further away from the airfield. These figures are for still air, add at least another 60ft to the height loss to allow for the surprise factor (i.e. in the 5-6seconds after the rope break, allowing for reaction times, and time to stabilise speed before turning). That is your level sink rate is 600fpm (i.e. 10 feet per second down), hence over 6 seconds, you would descend 60 feet). I will let people go figure what course of action they would decide. I sincerely hope that people have this all thought through when they do their pre-take-off checks, always(hint: it is under O for outside, obtacles and options). I have my flame suit on, and I am prepared for feedback re the maths ___ Aus-soaring mailing list Aus-soaring@lists.internode.on.net To check or change subscription details, visit: http://lists.internode.on.net/mailman/listinfo/aus-soaring
Re: [Aus-soaring] Maths and rope breaks
Hey Michael I was just being smart, suggesting that instinct should be inbuilt... maths only for those that like figures. Having said that, your maths is interesting... Imagine this, at the end of the 180 turn, if (but its not ) still at 60 deg bank, the wingtip is going to be about 300 ft away from the ground.. That should get them out of the club house to watch And a 180 only gets you going the other way, still over the next door paddock. If you were to use a procedure turn to get you lined up, you can add another 2 X 90 deg turns, and a roll of 120 deg. Youv'e really got their attention now ! Pulling the bung at 400 ft.. not much safety space And no, I don't know how to teach it realistically Cheers Col Texler, Michael wrote: I was by no way suggesting that one does the maths whilst in flight. It is used as the justification for performing such manoevures! Ok, radius of turn is given by R=V*V/(g*tan(bank)) R is radius in metres V is given in metres per second g is acceleration due gravity = 9.81 m/s/s Bank = angle of bank (AOB) in degrees (0=level) To convert knots to metres per second use: Airspeed in knots * 0.515 =metres/second. Given an example sink rate (i.e Bergfalke IV) at zero angle of bank at 60 KIAS as -3m/s (almost 600fpm down), making an approximation that the sink rate for a particular angle of bank is = 1/cos(bank). So at 30 degree AOB, the sink rate is -3.5m/s At 45 degree AOB, the sink rate is -4.2m/s At 60 degree AOB, the sink rate is -6 Hence pluging in values: At an airspeed of 60 knots AOB = 30, radius of turn is 552 feet = circling diameter of 336 metres AOB 45, radius = 319 feet, = circling diameter of 194 metres AOB 60, radius = 184 feet, = circling diameter of 112 metres The distance to travel half way around these circels (180 degree turn) is pi * diameter, time required to go the distance is distance travelled / airspeed AOB=30, distance=529m, time required=17secs, height loss (at sink of 3.5m/s) = 194 feet, diameter 336m AOB=45, distance=305m, time required=10secs, height loss (at sink of 4.2m/s) = 137 feet, diameter 194m AOB=60, distance=176m, time required=6secs, height loss (at sink of 6m/s) = 112 feet, diameter 112m Remember that the wider the diameter of the turn, you will have to turn through more than 180 degrees to get back to the strip, because the shallower turn will carry you further away from the airfield. These figures are for still air, add at least another 60ft to the height loss to allow for the surprise factor (i.e. in the 5-6seconds after the rope break, allowing for reaction times, and time to stabilise speed before turning). That is your level sink rate is 600fpm (i.e. 10 feet per second down), hence over 6 seconds, you would descend 60 feet). I will let people go figure what course of action they would decide. I sincerely hope that people have this all thought through when they do their pre-take-off checks, always(hint: it is under O for outside, obtacles and options). I have my flame suit on, and I am prepared for feedback re the maths ___ Aus-soaring mailing list Aus-soaring@lists.internode.on.net To check or change subscription details, visit: http://lists.internode.on.net/mailman/listinfo/aus-soaring ___ Aus-soaring mailing list Aus-soaring@lists.internode.on.net To check or change subscription details, visit: http://lists.internode.on.net/mailman/listinfo/aus-soaring
Re: [Aus-soaring] Maths and rope breaks
Could teach it in a Simulator :-) *plug plug* - Original Message - From: Colin Collyer [EMAIL PROTECTED] To: Discussion of issues relating to Soaring in Australia. aus-soaring@lists.internode.on.net Sent: Thursday, September 11, 2008 2:25 PM Subject: Re: [Aus-soaring] Maths and rope breaks Hey Michael I was just being smart, suggesting that instinct should be inbuilt... maths only for those that like figures. Having said that, your maths is interesting... Imagine this, at the end of the 180 turn, if (but its not ) still at 60 deg bank, the wingtip is going to be about 300 ft away from the ground.. That should get them out of the club house to watch And a 180 only gets you going the other way, still over the next door paddock. If you were to use a procedure turn to get you lined up, you can add another 2 X 90 deg turns, and a roll of 120 deg. Youv'e really got their attention now ! Pulling the bung at 400 ft.. not much safety space And no, I don't know how to teach it realistically Cheers Col Texler, Michael wrote: I was by no way suggesting that one does the maths whilst in flight. It is used as the justification for performing such manoevures! Ok, radius of turn is given by R=V*V/(g*tan(bank)) R is radius in metres V is given in metres per second g is acceleration due gravity = 9.81 m/s/s Bank = angle of bank (AOB) in degrees (0=level) To convert knots to metres per second use: Airspeed in knots * 0.515 =metres/second. Given an example sink rate (i.e Bergfalke IV) at zero angle of bank at 60 KIAS as -3m/s (almost 600fpm down), making an approximation that the sink rate for a particular angle of bank is = 1/cos(bank). So at 30 degree AOB, the sink rate is -3.5m/s At 45 degree AOB, the sink rate is -4.2m/s At 60 degree AOB, the sink rate is -6 Hence pluging in values: At an airspeed of 60 knots AOB = 30, radius of turn is 552 feet = circling diameter of 336 metres AOB 45, radius = 319 feet, = circling diameter of 194 metres AOB 60, radius = 184 feet, = circling diameter of 112 metres The distance to travel half way around these circels (180 degree turn) is pi * diameter, time required to go the distance is distance travelled / airspeed AOB=30, distance=529m, time required=17secs, height loss (at sink of 3.5m/s) = 194 feet, diameter 336m AOB=45, distance=305m, time required=10secs, height loss (at sink of 4.2m/s) = 137 feet, diameter 194m AOB=60, distance=176m, time required=6secs, height loss (at sink of 6m/s) = 112 feet, diameter 112m Remember that the wider the diameter of the turn, you will have to turn through more than 180 degrees to get back to the strip, because the shallower turn will carry you further away from the airfield. These figures are for still air, add at least another 60ft to the height loss to allow for the surprise factor (i.e. in the 5-6seconds after the rope break, allowing for reaction times, and time to stabilise speed before turning). That is your level sink rate is 600fpm (i.e. 10 feet per second down), hence over 6 seconds, you would descend 60 feet). I will let people go figure what course of action they would decide. I sincerely hope that people have this all thought through when they do their pre-take-off checks, always(hint: it is under O for outside, obtacles and options). I have my flame suit on, and I am prepared for feedback re the maths ___ Aus-soaring mailing list Aus-soaring@lists.internode.on.net To check or change subscription details, visit: http://lists.internode.on.net/mailman/listinfo/aus-soaring ___ Aus-soaring mailing list Aus-soaring@lists.internode.on.net To check or change subscription details, visit: http://lists.internode.on.net/mailman/listinfo/aus-soaring ___ Aus-soaring mailing list Aus-soaring@lists.internode.on.net To check or change subscription details, visit: http://lists.internode.on.net/mailman/listinfo/aus-soaring
Re: [Aus-soaring] Maths and rope breaks
On a parallel note... I always loved the bit of the C Certificate which requires you to show an entry into and recovery from a spin - that can be viewed from the glider or the ground. Wo while watching, the instructor will probably not offer a C- Certificate from the student who can't recover from the spin. Scott ___ Aus-soaring mailing list Aus-soaring@lists.internode.on.net To check or change subscription details, visit: http://lists.internode.on.net/mailman/listinfo/aus-soaring
Re: [Aus-soaring] Maths and rope breaks
Michael, I'm sure Anthony thinks his Bergie goes better than that. You have also not shown that 60 degrees is a minimum height loss just lower than 30 and 45 degrees. I take it you aren't a fan of a quick pull to vertical, stall turn and recover from dive going in the opposite direction with minimum offset? Thre's the sound of crickets chirping here from the instructors who were vocal about doing low altitude practice rope breaks. Surely somebody will be brave enough to give us an answer? Mike Borgelt Instruments - manufacturers of quality soaring instruments phone Int'l + 61 746 355784 fax Int'l + 61 746 358796 cellphone Int'l + 61 428 355784 Int'l + 61 429 355784 email: [EMAIL PROTECTED] website: www.borgeltinstruments.com ___ Aus-soaring mailing list Aus-soaring@lists.internode.on.net To check or change subscription details, visit: http://lists.internode.on.net/mailman/listinfo/aus-soaring
Re: [Aus-soaring] Maths and rope breaks
Hey Mike A stall turn from level flight at 'normal' speed.. Ill come outside and watch that. In aero modeling, we'd bring a plastic bag for the bits too ! Cheers Col Mike Borgelt wrote: Michael, I'm sure Anthony thinks his Bergie goes better than that. You have also not shown that 60 degrees is a minimum height loss just lower than 30 and 45 degrees. I take it you aren't a fan of a quick pull to vertical, stall turn and recover from dive going in the opposite direction with minimum offset? Thre's the sound of crickets chirping here from the instructors who were vocal about doing low altitude practice rope breaks. Surely somebody will be brave enough to give us an answer? Mike Borgelt Instruments - manufacturers of quality soaring instruments phone Int'l + 61 746 355784 fax Int'l + 61 746 358796 cellphone Int'l + 61 428 355784 Int'l + 61 429 355784 email: [EMAIL PROTECTED] website: www.borgeltinstruments.com ___ Aus-soaring mailing list Aus-soaring@lists.internode.on.net To check or change subscription details, visit: http://lists.internode.on.net/mailman/listinfo/aus-soaring ___ Aus-soaring mailing list Aus-soaring@lists.internode.on.net To check or change subscription details, visit: http://lists.internode.on.net/mailman/listinfo/aus-soaring
Re: [Aus-soaring] Maths and rope breaks
I take it you aren't a fan of a quick pull to vertical, stall turn and recover from dive going in the opposite direction with minimum offset? Of course, that is the best way to obtain the maximum benefit from dynamic soaring. Kevin ___ Aus-soaring mailing list Aus-soaring@lists.internode.on.net To check or change subscription details, visit: http://lists.internode.on.net/mailman/listinfo/aus-soaring
