Temperature and the ASI

11 Answers

1. 
   

   
   

   John D. Collins on Mar 15, 2011

   For a given power setting and altitude and baro pressure, the indicated airspeed would be higher on a cold day than a warm day. This is due to the denser air.  As you noted, you will cruise at a lower true airspeed because of the increase in drag, but you will be falsely happier about it because of your higher indicated airspeed.

    

   Your analysis is correct.  I remember taking off at Lake Tahoe on a hot day in a loaded Cherokee 6.  I did a full power runup and leaned for best power.  The runway is over 8 thousand feet long at an elevation of around 6200 feet.  Applied power, and initial acceleration was fair, finally the airspeed indicator was off the peg, 40 Kts, 45 Kts, … 50 Kts, …… 55 Kts, …….. 56 Kts,  …….. 56.5 Kts, ……….. 56.75 Kts and after what seemed an eternity it got up to the liftoff speed.  I circled over the lake on the east side and used the up rising air near the mountains to gain sufficient altitude to cross over the Sierra’s and head south westbound to my destination at San Jose.

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2. 
   

   
   

   Wes Beard on Mar 16, 2011

   The effects of temperature and pressure are cancelled out on the airspeed indicator.  The ASI, as we know, reads indicated airspeed in either knots or mph.  I have to disagree with John.
    
   To prove this point, I need to go back and explain how the airspeed indicator works.  You can read about it in the Instrument Flying Handbook starting on page 3-8.
    
   The airspeed indicator measures the difference between the RAM air (pitot) and the ambient air pressure (static).  If the air is colder, both the pitot and static pressures are increased the same value and if the air is warmer, both systems are decreased the same amount.  With everything being constant except for air temperature and pressure, the difference between the pitot pressure and the static pressure will remain the same.
    
   It is this reason why we rotate at the same rotation speed (indicated) when taking off from a sea level airport or from a mountaineous airport at 8000′ MSL.  It is also the same reason why we land at the same indicated airspeed whether at sea level or in the mountains.
    
   Density altitude, which is MSL altitude corrected for nonstandard pressure and nonstandard temperature, plays a big role in aircraft performance.  The true airspeed will be different for a sea level airport versus a 8000′ mountaineous airport but the indicated airspeed will not.  The airplane will have a much longer takeoff and landing roll but the indicated speed at which you rotate or land does not change.
    
   For question #2, the rate at which the indicated airspeed changes on takeoff or landings is dependent on the density altitude but the actual indicated airspeeds are independent of density altitude.  So yes, on hotter days the airspeed indicator will move slower than on colder days.
    
   I hope this answers your question.

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3. 
   

   
   

   John D. Collins on Mar 16, 2011

   Wes,

    

   From the cruise performance chart for my Bonanza, at fixed power settings of 75%, 65%, 55%, and 45% power at altitudes in 1000 foot increments to 16000 feet, the chart lists performance for three temperatures: ISA -20C, ISA, and ISA +20C.  It lists both the CAS and TAS. At the higher altitudes, the charted power is grayed out indicating that it is the maximum power available for the RPM specified. So ignoring the grayed out entries, the other entries are the same power setting at all the three temperatures.  In all cases, the TAS is highest at ISA+20, followed by the ISA value, and the lowest TAS is for ISA-20. On the other hand, the CAS values are reversed, with the highest CAS at ISA-20, followed by ISA, and lowest at ISA+20.

   Here is one example to show this effect although I could have picked any of the non grayed lines of any of the performance charts as they all follow the same pattern.  75% chart, 4000 feet, values in order of increasing temperature (ISA-20, ISA, ISA+20) and TAS-CAS: 165-162, 169-159, 172-157.  As you can see, TAS and CAS both change with temperature, TAS rises (165, 169, 172) with increasing temperature temperature and CAS decreases (162, 159, 157) with increasing temperature temperature. The converse of the last statement is that CAS rises with decreasing temperature.  The effect is not large, but it is there.  It is true that because the airspeed measures differential pressure, much of the effect is cancelled out, but not all of it because portion of the pressure that is measured by the pitot tube that is above the static pressure is not canceled out.

    

   You should be able to verify this same pattern on any other aircraft that has constant power performance charts and includes both TAS and CAS (or IAS) plotted at various temperatures.

    

   I stand by my statement in the first post.

    

    

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4. 
   

   
   

   John D. Collins on Mar 16, 2011

   Not to beat a dead horse, but for those that are mathematically inclined, from the ideal gas law in physics, Pv=nRT.  For our purposes, this can be rewritten as P= ρRT, where P is pressure, ρ (rho) is density or the amount of gas per unit volume (n/v), R is the Gas Constant, and T is the temperature in degrees Kelvin. The static pressure measured at the static port is a function of temperature (P1), the pitot dynamic pressure (P2) is also a function of temperature.  The airspeed indicator measures the difference between these two functions (P2-P1) and the difference is a function of temperature.

    

   As stated, most of the temperature effects are cancelled out, but not all of them.

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5. 
   

   
   

   Wes Beard on Mar 16, 2011

   Thanks John for the additional information.  For other readers some definitions are in order.

   Indicated Airspeed (IAS) – Measures the difference between the pitot and static pressures
   Calibrated Airspeed (CAS) – IAS corrected for position and installation error
   Equivalent Airspeed (EAS) – CAS corrected for compressibility
   True Airspeed (TAS) – EAS corrected for non standard temperature and pressure
   Groundspeed (GS) – TAS corrected for winds

   In most airplane operating handobooks there is a IAS / CAS conversion chart.  At higher airspeeds the difference between CAS and IAS is greater.  In the 182 POH downloaded from this site, the CAS is 5kts slower than IAS.
    
   Since we are talking only about indicated airspeed (IAS), is it possible that we haven’t taken the conversion from CAS back to IAS to compare apples to apples?  It will be interesting to see what it is in the Bonanza.

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6. 
   

   
   

   John D. Collins on Mar 16, 2011

   There is a small correction in the Bonanza between CAS and IAS in the cruise configuration (gear and flaps up) and using the standard static system.  At 80 knots they are equal.  At 120 kts IAS, CAS is 119; at 160 Kts IAS, CAS is 158 Kts. There isn’t a temperature correction between IAS and CAS, the difference is largely based on the slight geometry differences due to angle of attack.  There is a much greater difference between IAS and CAS when using the alternate static system or when the aircraft is in the landing configuration.

    

   I didn’t download the CAS to IAS values from the website, but I have a 1978 POH on the C182Q in my library and found the following differences between CAS and IAS. With the flaps up, CAS and IAS are the same at 80 Kts, at 120 Kts IAS, the CAS is 117 Kts, and for an IAS of 160 Kts, the CAS is 155 Kts.  Of course in a C182, you will never see an IAS of 160 Kts in level flight.

   The performance charts are organized differently in the C182 POH and each line uses a constant MP and RPM, so the power is not the same across the three temperatures, but the % power is shown for each temperature.  If you pick two entries from the same RPM that have the same % power, you can compare them for the different temperatures.  So at 4000 feet, with the RPM at 2300 RPM and the MP at 21 inches, at ISA-20 degrees, the entry shows 70% power and the TAS shows 132 Kts.  At the same % power and RPM, but at 22 inches MP, the chart for ISA+20 lists the TAS at 137 Kts.  Converting the 132 Kts at 4000 feet pressure altitude and -13 degrees C (ISA – 20) and 137 Kts at 27 degrees C (ISA +20), we get a CAS of 130 Kts at the colder temperature and 125 Kts at the warmer temperature.  All my calculations were done using the E6B function on my Garmin GPSMAP 696. Converting these speeds to an IAS using the conversion chart in the POH, you get 133 Kts IAS for the cold temperature and 128 Kts at the warmer temperature.  Once again, at the colder temperature, you will see a higher IAS, but will be disappointed with a lower TAS.

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7. 
   

   
   

   John D. Collins on Mar 16, 2011

   I am curious as to why my second post explaining my reasoning and offering straight forward facts is viewed negatively by some observer.  It is totally fact driven and not in any way personal. I take great pains not to get personal.  If you have objections to any of the facts or opinions I have offered, feel free to contest them as Wes has done.  I will always be happy to admit it if I am wrong and value any non personal criticism.

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8. 
   

   
   

   Brian on Mar 17, 2011

   John,
    
   I felt Wes did a great job pointing out the innacuracy in the following statement:
    
   “For a given power setting and altitude and baro pressure, the indicated airspeed would be higher on a cold day than a warm day. This is due to the denser air.” (Emphasis added by me.)
    
   Your second post focused on True AS, Calibrated AS, and finished with you standing by your first statement regarding Indicated AS. You’re right that you presented pure fact. However, I felt the facts were completely irrelevant to the discussion.
    
   Wes is right, IAS is the same for any given air density. Hence our v-speed remaining constant regardless of air density, temperature, altitude, etc. I think we can agree v-speed remain constant with altitude, also, which lends me to more confusion on your stance.
    
   Airspeed is calculated by subtracting static pressure, taken at the static port, from the total (not dynamic pressure, as your post on the ideal gas law suggests) pressure, taken at the pitot tube. The result is an instrument that represents numerical values based on a calculated dynamic pressure. It is because this instrument is based on this calculated dynamic pressure that we can expect consistent readings independent of air density.
    
   William Gracey wrote a very lengthy article on all the errors associated with the pitot static instruments called Measurement of Aircraft Speed and Altitude. It is over 200 pages, but it covers just about any error you will ever encounter with these instruments, how they are calibrated, limitations, etc. I think you’ll find it very informative on this particular subject. 
    
   Hope that helps,
    
   ~Brian
    
   P.S. I don’t typically give thumbs down without a reply. However, I’m on vacation and it looked like Wes had it covered quite well without my input. Sorry, I know how frustrating it can be to get negative feedback without any real feedback.
    

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9. 
   

   
   

   John D. Collins on Mar 21, 2011

   It seems the view of my initial post and subsequent posts has gotten worse and worse as time has gone by. Brian sent me a direct email with some good references from his website and I have been reading and studying. I agree with the following correction that Brian noted in his post: “Airspeed is calculated by subtracting static pressure, taken at the static port, from the total (not dynamic pressure, as your post on the ideal gas law suggests) pressure, taken at the pitot tube” and thus stand corrected. I sent a direct response to Brian commenting on portions of his post. As of yet, he has not replied, but he also indicated he was on vacation, so has more important things to do.

   The first paragraph of what I wrote to Brian is included below:

   Thanks for your post, it is very helpful, as is the referenced document. After rereading my initial post and Wesley’s post, it appears that we were talking past each other. We were answering different questions or at least different aspects of the same question. Wesley answered the question regarding the effect of temperature on takeoff and landing indicated airspeeds. I agree with everything he said with the sole exception of the second sentence in his post that reads: “I have to disagree with John.”

   I have a friend that was the Director of Aeronautics and Astronautics at the Naval Academy, Professor Emeritus Dr. Dave Rogers. I called him and discussed my first post with him at length. I sent him an email with the exact text of the post and a summary of our discussion and asked him to comment. I have included the contents of my email to him and his reply below.

   My email to Dr Dave Rogers follows:

   Dave,

   Thanks for taking the time this morning to discuss this with me.

   I wrote the following in response to a question on the effects of temperature and IAS and TAS.

   ”For a given power setting and altitude and baro pressure, the indicated airspeed would be higher on a cold day than a warm day. This is due to the denser air. As you noted, you will cruise at a lower true airspeed because of the increase in drag, but you will be falsely happier about it because of your higher indicated airspeed.”

   From our conversation, you noted the following:

   EAS (Effective Airspeed) can be used in place of CAS (Calibrated Airspeed) for low mach numbers such as the cruise speeds of my Bonanza or similar piston aircraft.

   IAS (Indicated Airspeed) is equal to CAS +/- installation errors and +/- instrument errors. In the case of a Bonanza, they are in the range of a knot or two at cruise speeds and don’t vary much over the normal range of cruise speeds.

   EAS can be related to TAS for the low mach numbers that the Bonanza is capable of cruising at by the equation: EAS = sqrt(density/density at sea level) * TAS.

   The ratio of the density of the air divided by the reference density is known as the density ratio. Since, the difference between CAS and EAS is small under the stated assumptions of TAS, CAS may be used in place of EAS. The difference between IAS and CAS are also small over the normal cruise speeds and do not vary much over the normal cruise range. The difference between IAS and CAS can be easily compensated for by using the manufacturer’s charts.

   With the assumption of a constant power setting, constant altitude, and barometric pressure, when the temperature decreases, EAS increases and therefore IAS increases.

   Any comments are appreciated, in particular whether my quoted statement is true or not.

   The reply from Dr Dave Rogers follows:

   G’day John,

   Your attempt to write an equation got garbled in the transmission. Hence, the correct symbols don’t show up at my end. However, your original statement I fixed them. However,

   “For a given power setting and altitude and baro pressure, the indicated airspeed would be higher on a cold day than a warm day. This is due to the denser air. As you noted, you will cruise at a lower true airspeed because of the increase in drag, but you will be falsely happier about it because of your higher indicated airspeed.”

   is correct.

   The other point to make is that the airspeed indicator is calibrated on the basis of the standard atmosphere.

   Dave Rogers

   David F. Rogers, PhD, ATP
   Professor of Aerospace Engineering (Emeritus) Annapolis, MD

   Rogers Aerospace Engineering & Consulting Annapolis, MD Over 50 years of experience http://www.nar-associates.com

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10. 
    

    
    

    Nathan Parker on Mar 26, 2011

    The idea that this subject is a discussion of the airspeed indicator is misguided, in my view.  That’s a red herring.

    The more fundamental issue is to understand that the IAS (EAS, really) of an airplane is controlled by the pitching moments that exist around the center of gravity; this is primarily controlled by the pilot using the elevator.  The longitudinal stability of the airplane will ensure that the airplane maintains the same lift coefficient (AoA, EAS) on the main wing.

    If an airplane encountered denser air, both the airspeed indicator and the aerodynamic surfaces of the airplane would experience an increase in dynamic pressure and the reaction of the airplane would be proportionate the change in the airspeed indicator.  The EAS would exceed that commanded by the elevator and the airplane would accelerate vertically and rotate nose up, seeking to restore the equilibrium EAS.

    Assuming no change in thrust (not realistic), the inclined flight path and increased drag of the temporarily increased EAS would slow the airplane back to the original EAS.  Since drag is proportionate to EAS, the airplane would resume level flight, after a suitable phugoid.  The TAS would be lower, due to the changes in air density.

    Any thrust changes will throw off this analysis. I know the original question assumed same power settings, but that’s not relevant.  That’s BHP; what’s relevant to actual performance is THP (thrust horse power), which takes into account propeller efficiency.  (I’m being charitable in assuming that we would adjust the power settings to maintain the same BHP in the new environmental conditions.)

    And if there is a change in thrust, thrust line affect the pitching moments around the airplane, hence affecting equilibrium EAS, but also any resulting cilmb/descent will have to be trimmed out, changing again the trimmed EAS.

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11. 
    

    
    

    Nathan Parker on Mar 26, 2011

    Let me add also that if the OP wasn’t really interested in aircraft behavior, perhaps the question would be better couched as something like “an airspeed indicator is attached to a choo choo train traveling at a constant speed on flat ground, when it encounters cooler air.  Will the airspeed indicator show any change?”
    In this case, the answer is “no”, except for the effect that temperature has on air density.  The air may, or may not, be denser in the cooler air, depending on how the other variables pertaining to the atmosphere change.  For instance, if surface pressure were lower, the air density might well be the same.  Whether that particular scenario is likely to occur becomes a discussion of atmosphere dynamics, rather than airspeed indicators, IMO. 
    Most likely, though, the cooler air will be denser and the airspeed indicator will show an increase.  We’ll take the choo choo train’s constant ground speed as equivalent to its TAS, so we’ll see a smaller difference between IAS and TAS, as you’d expect in denser air.

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