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There is a saying that your audience will halve for every equation you put in a piece of writing. Well, in this case I am going to make an exception and go through the detailed derivation of the Breguet Range equation. The reason for doing this is that the maths is not very difficult but the implications of the equation are known to every pilot on earth and everyone interested in flight should know about it. Simply put, the Breguet range equation tells engineers how far and airplane can fly given a certain set of parameters, and therefore greatly influences the design of modern jet engines and airframes.

A central aspect of flying further for the same amount of fuel is maximising the lift to drag ratio of your wings and airframe. Optimising this ratio gives the maximum aircraft weight (=lift at steady horizontal flight) that can be kept in the air for a given amount of engine thrust (=drag at steady horizontal flight). However, this parameter is not the primary optimum for commercial flight. Instead one wants to fly the furthest possible distance with one fuel filling. Thus to achieve the maximum possible range the quantity to be optimised is the product of flight speed ( U ) with lift ( L ) to drag ( D ) ratio . For most long-haul journeys (~12 hours) the most time consuming part of the journey, and therefore most critical for fuel consumption is the cruise condition. During cruise conditions the band of altitudes that the airliner travels through does not vary greatly such that the local speed of sound where T is the local static temperature, does not vary greatly. Consequently optimising the Mach Number times the lift to drag ratio is virtually the same.

Figure 1 shows experimental data of this parameter versus the lift-coefficient for a Boeing 747-400 at 35,000 ft. At each Mach number L/D rises to a maximum until further increase in lift coefficient leads to stall of the aerofoil. At lower flight speeds the boundary layer separation will occur naturally towards the trailing edge but as we approach a flight speed of Mach 1 shock waves also come into play.The graph shows that for all cruise speeds the optimum value of occurs at a lift coefficient of about 0.5. The wing area S of an aeroplane is set largely by conditions at take-off and landing, such that it is hard to continually operate at a lift coefficient of 0.5 as the weight and therefore lift of the aeroplane decreases as fuel is burnt. To operate as close to optimum on can therefore decrease v , not very attractive, or decrease the density by flying at higher altitudes. Large airliners therefore typically start cruise at 31 000 ft or higher and then increase altitude in steps to fly at the optimum.

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Waze drivers don't have to toggle between its app and Spotify.

By David Kaplan Mar 14, 2017 12:44PM

Driving and music are natural companions, so it makes sense that apps powered by Waze and Spotify thatreflect navigating and listening would come together.

The partnership between Waze and Spotify allows users of either one to stay within a single app to access and control the functions of both.

The idea of embedding complementary functions from one app (or more) into another — think of airlines and hotel apps letting users access a ride-hailing service within their walled garden — is becoming more common.

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, sharing APIs makes a lot of sense for most brands that can promote useful and seamless accompaniment.

“No more awkward flipping back-and-forth between apps or ending your favorite Friday-in-traffic tune to find the quickest way to the grocery store,” Waze says in a blog post touting the arrangement with Spotify.

The Spotify icon is visible on Waze (if Spotify is installed on the usersdevice, of course). One tap opens Spotify and the last song you listened to starts playing automatically, while the Waze navigation experience is uninterrupted.

For those who start their drive with the Spotify app, a banner at the top of streaming app’s window will prompt users to “Start Waze Navigation” without having to exit from their playlist.

The combination also would seem to strengthen Waze’s and Spotify’s audience numbers. Spotify currently claims 100 million users (30 million of whom are paid subscribers, meaning that the rest are exposed to its audio ads). For its part, Waze has 70 million monthly global users.

Considering that Meyiert Chic Womens S925 Silver Zirconia Butterfly Drop Pendant Long Tassels Linear Stud Earrings Pf9jU7ll2
are now listening on mobile — and that music streaming ad revenue is worth $1.5 billion and expected to hita reported $7 billion by 2030 — the alliance could also help drive ad revenue for both.

Waze and Spotify were unavailable to comment on whether they would actively collaborate on ad sales, but it stands to reason that anything that generates more time-spent will impress marketers who advertise either platform.

At the moment, the audience who can access the dual functions will be a bit limited, as the combination is only available on Google Android devices (Waze is owned by Google).

Tags in this story: , Spotify , ,
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About The Author
David Kaplan @davidakaplan

A New York City-based journalist for over 20 years, David Kaplan is managing editor of GeoMarketing.com. A former editor and reporter at AdExchanger, paidContent, Adweek and MediaPost.

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