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Yes, I know that. I have a great book on the subject. There however where no plans to actually bomb the US drawn up. Nor was there a desire or plan to "invade". Even Hitler knew that if sn invasion of England was impossible, the US was out of question. I highly doubt Hitler even would have wanted that. His plans were always to the east.
Thrust-to-weight or power-to-weight has always been a critical parameter for aircraft engines. I don't think you can deny that the 1400 lb difference between the Me 262 and the P-80 would not make a significant impact to performance to either plane.
I disagree with regard to the generalization of the statement. If You rely it to Jumo-004B engines, I could agree. But already with -004A engines it´s difficult to follw and BMW-003 engines were significantly ahead in terms of servicability times, reliability, flameout resistence in acceleration and operator friendliness.I don't think any jet engines had good reliability during this period. I don't think the German engines had any special claim to reliability (MTBF), engine replacement availability, operator friendliness, or any other criteria related to overall jet operations.
Again, You are generalizing a problem related to Jumo-004B engines and project the issue on other designs. I have a He-162 operators manual right in front of me. I quote from the section of emergancy operation (p.22):I think the German engines had their share of problems like difficulty to start, flame-outs with rapid throttle movement, etc.
B. Durchstarten.
1. Schubdüsenschalter muß auf "S" stehen
2. Zügig Vollgas geben
3. Fahrwerk kann eingefahren bleiben
4. Wieder normal anfliegen und zur Landung ansetzen
Originally, the He-162A was intended for BMW-003A engines (Baubeschreibung from oct. 1944) but all serial planes were fitted with BMW-003E-2 (pilots operators manual, p.3). Thrust rating 1760lbs is 9500rpm, overrew is 9800rpm. See the soviet trials on two of the He-162, they received.The only references I have shows 1760 lbs, but I can't say they are unimpeachable(...)
Apparently the 007 did not exist in 1945. I have no information on the 016.
Thanks that You referred to this issue. Are You aware that BMW-technicians under Karl Prastl rebuildt the BMW-018 in 1945 (OKB-I) on order of the soviet occupational forces in Eastern Germany? The designers first were tasked with BMW-003C/D and then had to basically "recreate" the BMW-018 with not all documentation surviving the war and all toolings destroyed. They benchtested the engine in oct. 1946 in Spandau/ near Berlin, roughly two years after the first prototype was destroyed in an air raid. Altough the engine was not put into production, it offered the soviets valuabel insights in high performance axial jet engine design.I think the program was a mess in 1945, if it existed at all. However, the BMW work certainly turned into a modern turbojet engine in France, one of my criteria for the evaluating the viability of war designs.
It seems that Germany made two mistakes in jet engine development (the allies made a few mistakes themselves) the first being to ignore the simpler and less exotic metal intensive centrifugal compressor engine, and two, cancelled the more efficient and lighter HeS 30 engine. It is interesting to note that the HeS 30 had a similar development and performance as the Westinghouse J-30 engine which first ran March, 1943 (the first run of the HeS 30 resulted in a redesign and did not run to full rpm until Oct., 1942). The axial flow J-30 engine ran the first time surprising the engineers. At that time there was little funding and the engine did not start flying test bed activity until Jan, '44. The engine developed 1500 lbs of thrust with a 2.2 thrust to weight ratio.As far as thust-to-weight ratio goes, I already pointed out that Schelp choosed a less optimal solution over a more advanced to assure it´s functionality and mass production. Germany aleady had a 1:2.2 ratio engine running in 1942, the axial HeS030, developing 1895lbs of thrust while weighting only 860lbs (benchtested feb 1942, flighttested Nov 1942). So appearently, thrust-to-weight ratio were not critically important paramters in selection of further development -at least in this period.
I have read that CD0 for the P-80 is quite a bit less than the Me 262 indicating the aircraft design is cleaner which makes sense with the embedded engine. Some comment was made as to inefficiencies of the inlets that reduced thrust and slowed the aircraft down to the Me 262 levels. This also makes sense since inlet and duct design is a sophisticated effort which would have been in its infancy in the 1940s. Still, the P-80 did reflect a more advanced and flexible design. The only real advantage the Me-262 had was the accidental help of slightly swept wing which was the result of fixing a design fault.As far as Me-262 and P-80 goes, the difference in weight of the -262´s engines are offsetted by better integration and high speed optimization of the airplane. Performance is not different between both.
Not enough to argue about but my calculations show the opposite. I don't like to use max weight but rather loaded weight, anyway, this certainly within error rate.Speed is roughly identic and the thrust-to-weight ratio is actually slightly favours the -262A (0.28 vs 0.26 at max. gross weight).
I disagree with your conclusion here. While I do think higher dive speed capability (due to higher Mach limit) is important to lose or catch an enemy, I do not think it is more important than altitude. The P-80 has a ceiling advantage giving it a great energy advantage and immunity. During the Korean War, the Mig-15 was unable to exceed the speed of sound even going straight down in full power. The F-86 was capable and did exceed the speed of sound in descent. However, the Mig-15 had ceiling advantage over the F-86 of only 3000 ft. This caused significant problems for F-86 in that the Mig would fly above them and attack or not any time they wanted. Also, they could also climb up to avoid an attack. Most analyst consider these two planes equal in performance. The P-80 has over a mile higher ceiling, which would give it a significant energy advantage.I can see advantages for the P-80 in roll and service ceiling, though not at limiting Mach number, which represents in my opinion a more critical design parameter for a first generation jet (0.80 as opposed to 0.84).
Sorry, this is all Greek to me.I disagree with regard to the generalization of the statement. If You rely it to Jumo-004B engines, I could agree. But already with -004A engines it´s difficult to follw and BMW-003 engines were significantly ahead in terms of servicability times, reliability, flameout resistence in acceleration and operator friendliness.
I think the German engines had their share of problems like difficulty to start, flame-outs with rapid throttle movement, etc.
Again, You are generalizing a problem related to Jumo-004B engines and project the issue on other designs. I have a He-162 operators manual right in front of me. I quote from the section of emergancy operation (p.22):
B. Durchstarten.
1. Schubdüsenschalter muß auf "S" stehen
2. Zügig Vollgas geben
3. Fahrwerk kann eingefahren bleiben
4. Wieder normal anfliegen und zur Landung ansetzen
That´s quite different to the careful operation of the -004B, whiches RPM shouldn´t drop below 7000 otherwise extreme care has to be applied to prevent turbine blade burnout. The difference was in design.
I would not bet on the fact that these engines were more reliable than Allied engines, maybe the J-33. I would have to see the failure rates including the Goblin used on the Meteor. One guy's opinion who I don't know but he has done research as a fellow at the US National Air and Space Museum follows.
From work by Dr. Daniel Uziel
"To sum things up, German jet engine development suffered from two fundamental flows:
1. The Germans tried to rush jet technology into service, but by concentrating their efforts from an early stage on the axial-flow design they skipped an important evolutionary stage. Huge investments in axial-flow engine R&D could not overcome all the technical difficulties involved in its development. Money could not buy, for example, the special metals required for the heat-resistant parts. The British started investing large amounts of money in Whittle's project only in 1940. It helped them close the gap with the Germans only because their engine was less complicated. As a result, at the end of WWII British jet engines were less modern, but more reliable, while German engines were more advanced, but less reliable.
2. Over-optimism regarding the quick maturing of advance technologies is a striking feature of German WWII leadership. It is especially evident in the jet story. For instance, in 1940 the Air Ministry planned to introduce a jet fighter into operational service by the end of 1942. It was a ridiculous notion as any aeronautical engineer at the time knew well it will take between two and three years to complete the development of a conventional fighter not to mention a revolutionary new type of aircraft. "
This tends to be my feelings also although I don't think any jet engine in this era had any claim to fame for reliability
The only Russian site I found shows the engine producing 1763 lbs thrust (800 kg)See the soviet trials on two of the He-162, they received.
Heinkel 162 - Salamander Jet Fighter- Interceptor - Luftwaffe
I don't doubt what you have said. I am sure you have better data than I have.
My comment on the 007 not existing in relation to 1945 was because it was cancelled. I didn't mean to imply it never existed.The dual flow, DB-007 was running 1943 and later was abandoned by Schelp and DB engaged work on the DB-017.
I ordered this right before I read your recommendation. Thanks for the recommendation; it tells me I didn't waste my money.Anthony Kay has more details on this jet engine in his book.
I would agree.The RR-Nene and Dervent-V were perhaps the best-overall-engines to see service in the mid/late 45´s, all factors considered.
I agree with this except that I don't think transonic knowledge came into play with the Me-262, just sound engineering and excellent aerodynamic design work.But does this hands any advantage to the allies wrt a jet case? I don´t think so. The advantage was mostly wasted by suboptimal aircraft design and lack of knowledge in the transsonic realm.
I think that by late '45 early '46 both the P-80 and Vampire would be operationally equivalent to the Me-262. The Meteor would be a bit later.It was not until the late 40´s that the allies had something which could beat the then contemporary version of the Me-262.
I think that, had the war continued, it definitely would have. Remember America built the P-40 up till 1944. It would have continued to develop different sources of fighters.And it´s highly unlikely, that the this airplane, the swept wing P-86 would have been produced given the fact that the straight wing version XP-86 didn´t offered better performance than the rather ill fated P-84.
You are correct in limiting Mach number but this is a minor player in the balance of fighters. If it played a big part, the Spitfire would have been unbeatable. The Me 262 did not have the performance advantage in speed, climb, or ceiling to clearly beat the P-80 during this period so this argument is moot. I have already discussed the advantages/disadvantages of dive speed to ceiling in my F-86 vs. Mig-15 comments. By the way, since the P-80 was cleaner, it probably had a better initial dive speed advantage although the Me 262 would eventually catch up.This graph shows the limiting Mach number of known airplane designs of the allies and Germany. It´s appearent that it took until the advent of the swept winged XP-86 to beat clearly the Me-262A.
I seem to be missing a graph here. I don't see anything showing thrust to weight. Again, max gross weight is not a good reference in that it punishes designs for load carrying ability. Ideally it is best to start with empty weight and add equal loads like pilot and equivalent fuel and armament. However, this data is often hard to get, but operation gross weight can be used. The data I have shows operational gross weight of the Me 262 as being 13,250 lbs, the P-80 operational gross weight of 11,700. However, the P-80 carries about 250 gallons less fuel which would make, if corrected, the operational weight of both aircraft the roughly same (however it is interesting to note that the range of the P-80 on full internal fuel is about the same as the Me 262 on full fuel even though the P-80 fuel load is quite a bit less). Thrust to weight is about the same except maybe better for the P-80 if equivalent fuel to performance weight is considered.This graph shows the development of thrust-to-weight ratio at max. gross weight for these airplanes. The USAAF does defenitely not benefit at all from their engines with better thrust-to-weight ratio. The RAF does, however, with the Dervent-V driven Meteor Mk. IV kicking ass.
This chart seems wrong in that it shows year to speed, not year to altitude.The final graphs shows speed at best altitude vs prototype date (The swept wing XP-86 beeing excluded but the straight wing XP-86 is within).
I agree with this observation. The YP-80A makes at comparable or less netto thrust more speed at Sea Level, implying a lower CD0 for the airframe. There are losses for duct and intake , though this will remain difficult to quantify (f.e. Messerschmidt made tests using a -262A with various 8 to 11ft long intake pipes and measured a loss of min 6% thrust). This changes with altitude as Mach compression raised drag becomes more and more an issue. This is why the -262A -in average- is slightly faster at higher altitudes (12000ft and more). However, I consider the -262A aerodynamically more advanced. Because of the adoption of a Wing sweep in combination with thin airfoils, leading edge slats (to counter adverse low speed handling inherent to all swept wings) and partially movable elevator rather than trim tabs. Even if accidently, these elements were forward directed. Wing root mounts for the engines were considered, too, in combination with larger wingsweep and more powerful engines (HG-III), which eventually would make the plane capable for true transsonic operation, something the P-80 never was capable of.I have read that CD0 for the P-80 is quite a bit less than the Me 262 indicating the aircraft design is cleaner which makes sense with the embedded engine. Some comment was made as to inefficiencies of the inlets that reduced thrust and slowed the aircraft down to the Me 262 levels. This also makes sense since inlet and duct design is a sophisticated effort which would have been in its infancy in the 1940s. Still, the P-80 did reflect a more advanced and flexible design. The only real advantage the Me-262 had was the accidental help of slightly swept wing which was the result of fixing a design fault.
I will concede this point. But how much fight took place at over 40000ft altitude in ww2?The P-80 has over a mile higher ceiling, which would give it a significant energy advantage.
This is that sort of generalizations which I invested some efforts to avoid. What he is speaking about is basically the Jumo-004B state as of mid to late 1944. With adoption of film cooling, hollow blade cooling, and Tinidur heat resistent alloys, these problems were largely overcome, though others (harmonic vibrations) appeared instead. The BMW-003 was much better in reliability than the Jumo-004 (by ten times wrt average service lifetime!) but this details is completely missed by the author. BMW went so far to employ acoustians to study harmonic vibrations for the turbine blades with the result that the service lifetime was substantially increased. When the russians copied the BMW-003, they replaced Tinidur with domestic El steels, which cut the service lifetime of the jet engine down to 100 hours. Still sufficient for their purposes and favourable with other axial jet engines. The BMW-003 also had no issues with flameout caused by rapid throttle changes due to the accelerator valve which was missing in the Jumo.Money could not buy, for example, the special metals required for the heat-resistant parts. The British started investing large amounts of money in Whittle's project only in 1940. It helped them close the gap with the Germans only because their engine was less complicated. As a result, at the end of WWII British jet engines were less modern, but more reliable, while German engines were more advanced, but less reliable.
I guess so. But do not forget that the 1944 Me-262A is quite a bit different than a late 45 or early 46 one. The improvements mentioned earlier in this thread would represent a serious enhancement of capabilities of the jet A/C and I see no reason why they shouldn´t be applied in an apple vs apple comparison.I think that by late '45 early '46 both the P-80 and Vampire would be operationally equivalent to the Me-262.
The P84 had a significantly lower crit Mach due to it´s thick airfoil sections. Thus, any performance advantage would materialize only at Sea level altitudes where the distance to limiting Mach numbers is large. Low altitude would be avoided in air combat due to fuel consumption issues, range at high altitude in the P-80 and P84 was twice to three times higher than at Sea level. At high altitude, the 1948 P-84 with 5400lbs jet engine is not much faster than the 1944 state standart -262A and slightly slower than the [late -45] -262A with 10% uprated engines and minor aerodynamic improvements approved for mass production in feb. 45.I would not consider the P-84 as being "ill fated". It certainly had its problems but so did other jet aircraft. It took the Me 262 three years from first flight to being full operational, the same time it took the F-84, 1946 to 1949 when the D became operational. Aerodynamically it was impressive, reaching 611 mph on 3750 lbs thrust, less than the Me 262 and P-80A.
My perception differs here considerably. The comparison between Spitfire and jets is not entirely correct here. One of the reason lies in the fact that the difference between operating cruise speed in limiting Mach is much narrower for a jet than for a prop driven plane operating at any altitude.If it played a big part, the Spitfire would have been unbeatable. The Me 262 did not have the performance advantage in speed, climb, or ceiling to clearly beat the P-80 during this period so this argument is moot. I have already discussed the advantages/disadvantages of dive speed to ceiling in my F-86 vs. Mig-15 comments. By the way, since the P-80 was cleaner, it probably had a better initial dive speed advantage although the Me 262 would eventually catch up.
While the Germans gambled on the potentially more efficient axial engines, their technology limitations and material shortages put them at an engine disadvantage in 1945 that would hamper their more advanced aircraft designs. I don't think the axial engines caught up with the centrifugal engines until the Korean War. Even then, the Mig 15 KV-1 engine was 1312 lbs lighter than the F-86's J-47 at the same thrust. With the more powerful engines, the centrifugal compressors could be buried in the fuselage, somewhat offsetting the advantage of the more slender axial engines.
It is also interesting to note number of different jet engines and variety of technology available to the Allies as compared to the Germans.
Delcyros, where does your graph for limiting Mach numbers come from? I see no report number ... just a graph. Is it from a flight simulator or a real report? If so, by whom?
Not saying it is wrong, just wondering.
The GE J33 or the Nene was again much larger (+20%), essentially reached the size of the larger radial piston jobs, so it had to be put into the fuselage as it already grown out the wings. The next step would be an even larger engine and the fuselage starts to grow fatter, drag rises steeply and you are entering the area rapidly decreasing dividients and this point was already met in 1945. To achieve maximum speed a minimum fuselage cross section (~drag) is required.
I understand all you say and I am sure you are correct and that is the way things were. I guess I was offering a different scenario where there was encouragement to pursue a centrifugal engine and a manufacturer like Heinkel was given the task of build an airframe for a 4-5000 lb thrust engine and, because it was easier to build and manufacture, produce in quantity a high performing jet in late '43 what impact would it have. I don't really want to start a new thread here, just wondering.However, the design environment of the GAF called distinctly for airframes, whiches details of jet engine installation required external mounts to ease maintenance and allow for rapid replacement of worn out engines (see f.e. underwing mounts in He-280, Me-262, Ar-234 and He-162, the principal jet engined designs adopted for development in the early and mid war period. Only with the 1944 and later designed jet A/C little by little fuselage mounts became acceptable from a design point of view. We have to reckon with difficult working conditions and fear of technological failure in this period.
The He 178 didn't seem to have a problem with this, nor did the Americans with the P-59 which first flew just three months after the Me 262. Anyway, a burning engine on the wing will certainly encourage a pilot to exit the aircraft, so chances are it would be lost anyway. Did the Me 262 have a problem with burning engines? I suspect the primary reason for the pod mount was for maintenance and replacement reasons like the Boeing 707 vs the Comet. The maintenance and replacement of the engine on the P-80 was probably more difficult but not much. At least it wasn't on the plastic model TV-2 I put together as a kid.Leaking engines were quite common but in a fuselage mounted one this would determine the eventual loss of the airplane. Only when safety record became advantageous this requirement was finally dropped (Ho-229, Me-P1101, Ta-183 and -Flitzer, Ju-EF128, Hs-P135 and others). It was the ultimate reason for both Heinkel and Messerschmidt beeing forced to avoid fuselage mounts for their He-280 and Me-262, respectively.
In general, I agree. The Brits seem to do okay with their Meteor, however. The real advantage with the bigger engine is burying it in the fuselage, reducing the cross section significantly.However, with radial engines in external mounts, frontal diameter of the jet engines very soon becomes a critical design parameter. Thus, I remain convinced that the GAF got the compromise they desired most with axial jet engines in external engine nacelles.
However, Allied designers would not be idle either and by the time new engines appeared, most likely advanced Allied engines, such as the Nene with 25% more thrust could be installed into the P-80. And, with Kelly Johnson running the program, a swept wing P-80 would be out six months after the first sighting of a swept wing German fighter (I would guess a fixed wing P 1101).Wing root mounts for the engines were considered, too, in combination with larger wingsweep and more powerful engines (HG-III), which eventually would make the plane capable for true transsonic operation, something the P-80 never was capable of.
This is not the point. Higher altitude is higher energy and an area of safety and tactical advantage in that they could attack or not. Coming down the P-80 could easily reach their Mach limit which would still be faster than anything the Me 262 could reach in level flight. They would overtake the Mes and break up their formations and climb back up (they could out climb the Me at any altitude) and do it all over again, or just chase the Mes down to lower altitude where the P-80s would have better speed and climb. Chances are the Mes would pull away from the P-80s in the dive but still their attack on bombers would be broken.I will concede this point. But how much fight took place at over 40000ft altitude in ww2?
I can't really argue this point as I don't know. The BMW-003 seem to have too little an operational experience to make a judgment on reliability however.The BMW-003 also had no issues with flameout caused by rapid throttle changes due to the accelerator valve which was missing in the Jumo.
I already talked about the engines. Other than the slightly swept back wings of the Me 262 and Me 163, I do not believe an aircraft with the sweep levels necessary to significantly increase Mach limit had ever gone through any formal flight testing (they did have a aircraft under development that could evaluate this in the P1101) so rapid adaptation of the swept wing was questionable.I guess so. But do not forget that the 1944 Me-262A is quite a bit different than a late 45 or early 46 one. The improvements mentioned earlier in this thread would represent a serious enhancement of capabilities of the jet A/C and I see no reason why they shouldn´t be applied in an apple vs apple comparison.
It certainly had its problem, especially with engines. I don't have any sources to use to question you comment on high altitude flying. However, it did indeed have good low altitude performance and could out maneuver a Mig 15 at low altitude as reported by Col. Richard Burns at this siteThe P84 had a significantly lower crit Mach due to it´s thick airfoil sections. Thus, any performance advantage would materialize only at Sea level altitudes where the distance to limiting Mach numbers is large. Low altitude would be avoided in air combat due to fuel consumption issues, range at high altitude in the P-80 and P84 was twice to three times higher than at Sea level. At high altitude, the 1948 P-84 with 5400lbs jet engine is not much faster than the 1944 state standart -262A and slightly slower than the [late -45] -262A with 10% uprated engines and minor aerodynamic improvements approved for mass production in feb. 45.
"One day we got in a dog fight over North Korea and I ended up with a MIG on my tail. One of our guys yelled, 'You have a MIG right behind you,' he said. "I knew I could out fly him if I could get down on the deck. So I came down to 5,000 or 6,000 feet and started making tight, level turns. Any time we got in trouble with a MIG on our tail we'd do this and eventually the MIG would fly away," he said.
The only way these two planes could get close to their limiting Mach number is in a lightly loaded dive, i.e., no heavy maneuvering. Any yanking and banking would negate Mach limit as an issue. I have discussed how that this is important in escaping and engaging the enemy, but while the F-86 could easily out dive a Mig-15, the Mig 15 was still a real pest due to its higher ceiling and good maneuverability and was a formidable competitor. I do not believe the higher Mach capability was a war winning advantage over the P-80. I see the relationship of the Me 262 vs. the P-80 as similar to the F-86 vs. the Mig-15. With good low altitude capability and reasonable high altitude performance, especially in ceiling, I think that, in mass, like the Allies liked and had the capability to do, they would have quickly eliminated the Me 262 as a significant threat.At high altitude, where M=1.0 is around 660mph the P80 engages it´s limiting Mach number already at 528mph.
I don't think so. The not much larger Derwent were aerodynamically better located semi-submerged in the wing, probably mitigating the increased frontal area of the engine. I think the main culprit in drag was the large wing, 50% larger than the Me 262. The P-59, With a much aerodynamically (probably) better located engines but with a humongous wing 65% bigger than the Me 262, was still slow as a toad.The Derwent was already much (+20%) larger diameter (and thus drag) than German axials, which is why the Meteor was so much slower.
The J-48/Tay engine maxed out at 7250 lbs thrust dry and was the same diameter as the J-33/Nene, an impressive 45% increase in thrust and powered the 1953 F9F Cougar. At this time the axial engines actually caught up with the centrifugal engines in thrust and thrust to weight. The BMW 003/SNECMA ATAR engine generated 7490 lb thrust, dry, for the Super Mystere B.2 in 1955, with a thrust to weight ratio roughly two/thirds the J-48. And the ATAR was developed with the assistance of German engineers and scientist.The GE J33 or the Nene was again much larger (+20%), essentially reached the size of the larger radial piston jobs, so it had to be put into the fuselage as it already grown out the wings. The next step would be an even larger engine and the fuselage starts to grow fatter, drag rises steeply and you are entering the area rapidly decreasing dividients and this point was already met in 1945. To achieve maximum speed a minimum fuselage cross section (~drag) is required. Look at the Nene's history, a great centrifugal engine no doubt, but essentially it stuck right where it started, even the version in the MiG 15 did not improve much on its thrust.
Dead end? Yes, As was the Me 262. That does not mean they were not the right answer at the right time. The centrifugal engine was more than competitive until the advent of Mach aircraft, at which time the diameter became critical and efficiencies of the axial engines exceeded that of the centrifugal engines. This was approximately early to mid-fifties, even with German development.See the pattern here? Centrifugal jet engines were dead end and extremely limited development potentional for fighter applications,
This seems not to be true with the Nene-to-J-48 upgrade.basically the way they increased output meaningfully was increasing the size (diameter) of the engine.
I was an Avionic manager/engineer for 29 years working for a prime contractor company whose main customer was the military. I have designed and developed and had installed hardware for aircraft ranging from light supersonic fighter aircraft (F-5E, F-35), research aircraft (Tacit Blue) to heavy bombers (B-2) and heavy transport aircraft (Joint STARs). I can assure you that I have sweated blood for every pound for every program. I can also assure you that one of the main efforts of every program manager is a parameter line typically called weight management.Thrust to weight ratio is interesting and a good T/W is useful for improving climb, but does next to nothing to improve top speed, especially at jet top speeds, which was what jets were all about. Even T/W ratio had less importance with jets than with prop jobs since the jets made their best climb at about twice the speed than prop jobs where induced drag is far less dominant.