Hank vs Bonal

[bonal]

so here is one for the math guys. Hank and Bonal are both flying from point A to B and since the runway is 100 feet wide they feel like showing off and take off together. Hank likes to climb at 100mph and 1000fpm Bonal likes to climb at 120mph and gets 800fpm and both want to fly at the same altitude of 7500 feet. The airports are at sea level and its a 100 mile flight. Since both aircraft (airplanes) fly at 165mph true who would arrive first. Since Hank will reach his target altitude sooner how long would it take for him to catch Bonal.

Edited October 25, 2015 by bonal

[yvesg]

I am trying this answer: they will arrive at the same time.

Yves

[sleepingsquirrel]

The one with the best velocity made good to altitude will win. Provided Hank remembers to retract his gear. 

Cos (angle of climb)( speed)=VMG         highest VMG to altitude wins

[Little Runaway]

Trick question. Hank will never catch Bonal if they cruise at the same speed.

My Saturday evening math shows that Hank will arrive 24 seconds after Bonal, assuming they both instantly accelerate to cruise speed at the top of the climb. Total flight time: Hank, 39 minutes, 19 seconds. Bonal, 38 minutes, 55 seconds.

[sleepingsquirrel]

VMG to altitude for Hank is 99.4 MPH

VMG to altitude for Bonal is 119.6 MPH

AAronsn is correct Hank will never catch Bonal

Please my trig is rusty. and too sleepy to care 

[PTK]

Bonal will never catch up to Hank because Hank has traveled 2 more miles horizontal distance than Bonal upon reaching 7500!

Hank:

sin(θ)=7500/60000; θ=7.2°

Bonal:

sin(θ)=7500/48000; θ=9°

Horizontal distance traveled upon reaching 7500 altitude is cos(θ)·hypotenuse.

11.3 miles for Hank and 9 miles for Bonal.

 

Edited October 25, 2015 by PTK

[sleepingsquirrel]

Bonal travels 18.69 miles over the ground during the climb to 7500 feet.

Hank travels 12.36 miles over the ground during the climb to 7500 feet.

[Hank]

Hank is traveling today. Let him get home to paper and calculator . . .

Hey Bonal, how do you descend? I do it power on, just push for 500 fpm and trim the force away; I walk throttle back and mixture forward to maintain cruise MP & EGT. IAS is always 170-175 mph, groundspeed can be > 200 mph.

[sleepingsquirrel]

I confirm Hank arrives 23.4 second after Bonal. AAronson is correct.

The angles are 6.5 degrees for Hank and 4.3 degrees for Bonal.

 

Edited October 25, 2015 by sleepingsquirrel

[sleepingsquirrel]

Bonal will never catch up to Hank because Hank has traveled 2 more miles horizontal distance than Bonal upon reaching 7500!

Hank:

sin(θ)=7500/60000; θ=7.2°

Bonal:

sin(θ)=7500/48000; θ=9°

Horizontal distance traveled upon reaching 7500 altitude is cos(θ)·hypotenuse.

11.3 miles for Hank and 9 miles for Bonal.

 

1000FPM is a higher angle than 800FPM.  Bonals angle cannot be higher than Hanks.

[sleepingsquirrel]

Hank is traveling today. Let him get home to paper and calculator . . .

Hey Bonal, how do you descend? I do it power on, just push for 500 fpm and trim the force away; I walk throttle back and mixture forward to maintain cruise MP & EGT. IAS is always 170-175 mph, groundspeed can be > 200 mph.

In the spirit of this discussion We all know that Bonal's M20D model can't run the same cruise as Hank's retract. Now that PTK has spoken it doesn't matter if you both descend vertically at the same supersonic speed at your destination.

[sleepingsquirrel]

Let me start a crap storm on Mooneyspace!

What if Hank climbs to 7600 feet and gets on the "STEP" as he comes back to 7500 feet?

:

so here is one for the math guys. Hank and Bonal are both flying from point A to B and since the runway is 100 feet wide they feel like showing off and take off together. Hank likes to climb at 100mph and 1000fpm Bonal likes to climb at 120mph and gets 800fpm and both want to fly at the same altitude of 7500 feet. The airports are at sea level and its a 100 mile flight. Since both aircraft (airplanes) fly at 165mph true who would arrive first. Since Hank will reach his target altitude sooner how long would it take for him to catch Bonal.

 

Edited October 25, 2015 by sleepingsquirrel

[bonal]

Hank is traveling today. Let him get home to paper and calculator . . .

Hey Bonal, how do you descend? I do it power on, just push for 500 fpm and trim the force away; I walk throttle back and mixture forward to maintain cruise MP & EGT. IAS is always 170-175 mph, groundspeed can be > 200 mph.

depends on terrain but if I have smooth air I push for 300 to 500fpm and stay WOT and IAS is just under 180mph and for the record my D is converted

[sleepingsquirrel]

depends on terrain but if I have smooth air I push for 300 to 500fpm and stay WOT and IAS is just under 180mph and for the record my D is converted

Well that throws a monkey wrench into the whole problem ,retractable D models, two pilots descending at different rates (previously not in evidence)." Cats and dogs living together"

[bonal]

Well that throws a monkey wrench into the whole problem ,retractable D models, two pilots descending at different rates (previously not in evidence)." Cats and dogs living together"

lots of variables but if we descend at the same rate I would begin my descent 23.4 seconds sooner to 175mph but hank would close in again as we slow for the approach unless he implements turbo prop mentally and calls for a straight in to the run way.

[TWinter]

You guys are out of my league..I have enough trouble doing W/B on my own plane

[sleepingsquirrel]

Another variable I believe is the time to climb and  the increase in true airspeed as altitude from sea level to 7500 feet. This favors the least time spent in the climb (Hank) and more time at higher true airspeed. It is in all likelihood insignificant, but so is 23.4 seconds!  

If you hold constant indicated airspeed in the climb, the true air speed will increase as the air becomes less dense , correct? 

I'm sure if you fly an SR-71 this matters.

 

Edited October 25, 2015 by sleepingsquirrel

[sleepingsquirrel]

lots of variables but if we descend at the same rate I would begin my descent 23.4 seconds sooner to 175mph but hank would close in again as we slow for the approach unless he implements turbo prop mentally and calls for a straight in to the run way.

Yep, no one specified a safe landing. Hank could fly 185 MPH for a long final,185 over the numbers ! 

[cliffy]

Might be a fun formation clinic to T/O together, fly the trip and a formation landing :-)

AFAIK, there are only 2 stiff legged Ds left in the inventory. Mine is NOT one of them. I have suckum-ups installed also. 

Speed is a relative thing. All props are slow to me after thousands of hours in 727s and Lears :-)

 

 

[Immelman]

On a 100 mile flight, Immelman wins doing a yellow-arc cruise climb to 3000', if not less, and hauling a$$ all the way there. The key is the short flight distance.

[sleepingsquirrel]

Where is it I can purchase an all metal "how high do I climb for the distance I'm traveling with the lowest fuel burn in the shortest time" calculator. It must also be able to calculate a  speed  1.3  stall speed at landing weight which it automatically senses and a have landing pattern computer. I need it by Christmas!

Edited October 25, 2015 by sleepingsquirrel

[1964-M20E]

This goes to show you enjoy flying and the flight and forget about how long it takes on a 100 mile trip.

 

Just make sure you have enough fuel and weather that  meets your minimums.

 

 

 

 

[PTK]

Yes, Sleepingsquirel you're correct.

The climb angles are indeed 6.5° for Hank and 4.3° for Bonal. Using tan. I erroneously used sin and neglected to account for airspeed.

[sleepingsquirrel]

Yes, Sleepingsquirel you're correct.

The climb angles are indeed 6.5° for Hank and 4.3° for Bonal. Using tan. I erroneously used sin and neglected to account for airspeed.

HI, I made a few mistakes myself. I don't even know why I started to answer the initial question other than doing it for the fun. Aaronson was quick and correct he must be 25 years old! 

[Hector]

SOH CAH TOA